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JavaScript DIV Editing Destroys Functionality of Other Elements

So my website is built using a company's software called Inksoft which leaves me very little to work in the way of customization. So I have to do many workarounds.
Here is my site's homepage.
The header on top of the page only has two links right now. "Products" and "Design Studio". My goal is to add an "About Us" link and "Buyers Guide" to the header as well.
I cannot add new content to the header using Inksoft's backend. So I coded a workaround to replace the content of existing DIV's within the header to say and link to where I want them to go.
The only issue is, the responsive mobile-nav loses functionality when this is implemented. As seen here on this test page.
The test page has the About Us in the top header, added by the use of this code:
<script>
$("#header-nav-designs").html('<document.write="<li id="header-nav-studio"><font color="#000000">About Us</font></li>');
</script>
So, the simplified question is: how do I implement this code without losing the responsive functionality of the nav bar?

The jQuery .html function will replace the HTML inside the target element. If you want to just append the one value, you likely want to .append to the element.
In addition, you aren't setting the HTML to a valid html string. You probably just want to get rid of the <document.write=" at the beginning of the string. The rest of it looks fine with just a cursory glance.
So:
<script>
$("#header-nav-designs").append('<li id="header-nav-studio"><font color="#000000">About Us</font></li>');
</script>
Edit:
After looking at it a little more, it appears as though the $('#header-nav-designs') that you are selecting is already an <li> which means you need to either select the parent <ul> list or you can use the jquery .after function instead.
<script>
$("#header-nav-designs").after('<li id="header-nav-studio"><font color="#000000">About Us</font></li>');
</script>
And as someone else commented above, you are getting an error on the page. It appears as though you are trying to get an element with the id divID and the appending some html to it, but there is no element with the id divID and so you are getting an error saying that you can't read the property innerHTML of null as the call to document.getElementById is returning null (element not found).

Element id header-nav-designs witch your code is referring have CSS style on line 170:
#header-nav-designs {display:none;}
The element will be hidden, and the page will be displayed as if the element is not there. With display:none;
If I understand you correctly your code selector points to wrong element id. It should point $(".header-nav > ul"). Document.write is not needed inside jQuery you need to give only an valid html string as argument.
jQuery html function erase html that is all ready inside element and replace it with html string given as argument. You have to use append if you want to add more html but not remove what is allready in element.
$(".header-nav > ul").append('<li><font color="#000000">About Us</font></li>');
$(".header-nav > ul").append('<li><font color="#000000">Buyers Guide</font></li>');

jquery .load() and access to host page's scripts

I've read through a few posts here regarding this topic, but none seem to answer which method is the best for allowing sub-pages access to the host page's <script> section.
I load home.php, which has a menu displayed in one of its two <div> sections. The HTML for this menu is on home.php itself. The user is able to interact with buttons and dropdowns in the menu portion of home.php through scripts on home.php, like:
$("#graphsButton").click(function() {
if($(this).text()=="Graphs") {
$(this).html("<span><i class='fa fa-check-circle checked'></i> Graphs</span>");
graph = true;
} else {
$(this).html("<span>Graphs</span>");
graph = false;
}
});
After the user performs their initial operations, that larger menu is replaced by a smaller menu to provide the user more screen real-estate, using the following code:
function shrinkMenu() {
$('#search').html('');
$('#search').animate({
width: '4%'
}, 500);
$('#returnMain').animate({
width: '96%'
}, 500);
$('#search').load('smallMenu.php');
}
If the user wants the big menu back, on smallMenu.php I then have another <script> section with this code:
$('#growMenu').click(function () {
$('#search').html('');
$('#search').animate({
width: '20%'
}, 500);
$('#returnMain').animate({
width: '80%'
}, 500);
$('#search').load('largeMenu.php');
});
largeMenu.php contains a duplicate copy of the original HTML for the menu that loaded along with home.php, and visually, it looks exactly the same to the user.
As I toggle between large menu and small menu however, the <script> sections contained in home.php that pertain to the id tags in the original menu HTML that loaded with home.php no longer work.
In order to make it work, it seems that I would have to re-initialize all my plugins on each page load, and maintain 3 separate pages' <script> sections that are all duplicates of one another, and this seems very inefficient and probably not the best way to go about this.
Is there a better way for me to achieve the functionality I am trying to code here?
Update
My code looks like this at a high level:
<div class="searchParent" id="search">
<div class="return"></div>
<div class="menu">
<div class="largeMenu" id="largeMenu"></div>
</div>
</div>

What you are doing is fine by replacing the menu from a php file that contains a "partial view" which is your menu HTML. The partial view relies upon the parent page code, so you don't need to duplicate any code from the parent script into the partial view. The partial view can expect there is script code on the parent page it can be used with.
As I toggle between large menu and small menu however, the
sections contained in home.php that pertain to the id tags in the
original menu HTML that loaded with home.php no longer work.
The problem you are having though is that you need to ensure that the code on home.php that references these menus uses a parent container as its reference point instead of direct IDs. You are replacing elements (menus), so the bindings are lost when you do that unless you bind on a parent higher up the DOM that doesn't get replaced (remember that events bubble up).
From what I see in your code snippets, it looks like the menu is loaded into the #search container. So just ensure the code in home.php uses that container as the reference point, using something like on like this:
$('#search').on('click', '#graphsButton', function() {
// ...
});

Expand/Collapse Text

The code below works fine with ONE Reveal/Hide Text process
<div class="reveal">Click Here to READ MORE...</div>
<div style="display:none;">
<div class="collapse" style="display:none;">Collapse Text</div>
However if this code is duplicated multiple times, the Collapse Text shows up and doesn't disappear and in fact conflicts with the Expand to reveal even more text instead of collapsing as it should.
In this http://jsfiddle.net/syEM3/4/ click on any of the Click Here to READ MORE...
Notice how the Collapse Text shows up at the bottom of the paragraphs and doesn't disappear. Click on the Collapse and it reveal more text.
How do I prevent this and getting to work as it should?

The two slideDown function calls are not specific to the .reveal and/or .collapse that you are currently doing. i.e.
$(".collapse").slideDown(100);
will find all the elements with the class .collapse on the page, and slide them down. irrespective of what element you just clicked.
I would change the slideDown call to be relavant to the element you just clicked i.e. something like this
$('.reveal').click(function() {
$(this).slideUp(100);
$(this).next().slideToggle();
$(this).next().next(".collapse").slideToggle(100);
});

in your code
$('.reveal').click(function() {
$(this).slideUp(100);
$(this).next().slideToggle();
$(".collapse").slideDown(100);
});
$('.collapse').click(function() {
$(this).slideUp(100);
$(this).prev().slideToggle();
$(".reveal").slideDown(100);
});
this two rows doesn’t do what you want as they act on all elements of the specified class
$(".reveal").slideDown(100);
$(".collapse").slideDown(100);

When you do $(".collapse").slideDown(100);, jQuery runs slideDown on everything with the .collapse class, not just the one that's related to your current this. To fix this, refer to the collapse based on its location to $(this).
Do do this, use something like $(this).siblings(".collapse").slideDown(100);
Note that this particular selector will only work if you enclose each text block in its own div. With each text element in its own div, like you have it now, .siblings(".collapse"), which selects all the siblings of $(this) with the collapse class, will still select both of the collapse elements.

Okay, I think you should take a different approach to your problem.
See, jQuery basically has two purposes:
Selecting one or more DOM elements from your HTML page
manipulate the selected elements in some way
This can be repeated multiple times, since jQuery functions are chainable (this means you can call function after function after function...).
If I understood your problem correctly, you are trying to build a list of blog posts and only display teasers of them.
After the user clicks the "read more" button, the complete article gets expanded.
Keep in mind: jQuery selects your elements very much like CSS would do. This makes it extremely easy to
come up with a query for certain elements, but you need to structure your HTML in a good way, like
you would do for formatting reasons.
So I suggest you should use this basic markup for each of your articles (heads up, HTML5 at work!):
<article class="article">
<section class="teaser">
Hey, I am a incredible teaser text! I just introduce you to the article.
</section>
<section class="full">
I am the articles body text. You should not see me initially.
</section>
</article>
You can replace the article and section elements with div elements if you like to.
And here is the CSS for this markup:
/* In case you want to display multiple articles underneath, separate them a bit */
.article{
margin-bottom: 50px;
}
/* we want the teaser to stand out a bit, so we format it bold */
.teaser{
font-weight: bold;
}
/* The article body should be a bit separated from the teaser */
.full{
padding-top: 10px;
}
/* This class is used to hide elements */
.hidden{
display: none;
}
The way we created the markup and CSS allows us to put multiple articles underneath.
Okay, you may have noticed: I completely omitted any "read more" or "collapse" buttons. This is done by intention.
If somebody visits the blog site with javascript disabled (maybe a search engine, or a old mobile which doesn't support JS or whatever),
the logic would be broken. Also, many text-snippets like "read more" and "collapse" are not relevant if they don't actually do anything and are not part of the article.
Initially, no article body is hidden, since we didn't apply the hidden css class anywhere. If we would
have embedded it in the HTML and someone really has no JavaScript, he would be unable to read anything.
Adding some jQuery magic
At the bottom of the page, we are embedding the jQuery library from the google CDN.
<script src="//ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js"></script>
This is a best practice and will normally speed up your page loading time. Since MANY websites are embedding
jQuery through this URL, chances are high that its already in the visitors browser cache and doesn't have
to be downloaded another time.
Notice that the http: at the beginning of the URL is omitted. This causes browsers to use the pages current protocol,
may it be http or https. If you would try and embed the jQuery lib via http protocol on a https website, some browsers will refuse to download the file from a unsecure connection.
After you included jQuery into the page, we are going to add our logic into a script tag. Normally we would
save the logic into a separate file (again caching and what not all), but this time a script block will do fine.
Finally some JavaScript
At first, we want to hide all elements with the css-class full, since only teasers should remain displayed. This is very easy with jQuery:
$('.full').hide();
The beginning of the script $('.full') tells jQuery: I need all elements with the CSS-class full. Then we call a function on that result, namingly hide() which purpose should be clear.
Okay, in the next step, we want to add some "read more" buttons, next to every teaser. Thats an easy task, too:
$('.teaser').after('<button class="more">Read more</button>');
We now select every element with the css-class teaser and append some HTML code after() each element - a button with the css-class more.
In the next step, we tell jQuery to observe clicks on every one of this freshly created buttons. When a user has clicked, we want to expand the next element with the css-class full after the clicked button.
$('.more').on('click', function(){
//"this" is a reference to the button element!
$(this).slideUp().next('.full').slideDown();
});
Phew, what did we do here?
First, we told jQuery that we wanted to manipulate this, which is a reference to the clicked button. Then we told
jQuery to hide that button (since its not needed anymore) slowly with slideUp().
We immediately continued telling jQuery what to do: Now take the next() element (with the css-class full) and make it visible by sliding it down with slideDown().
Thats the power of jQuerys chaining!
Hiding again
But wait, you wanted to be able to collapse the articles again! So we need a "collapse" button, too and
some more JavaScript:
$('.full').append('<button class="collapse">Collapse text</button>');
Note: we didn't use the after() function to add this button, but the append() function to place the button
INSIDE every element with the css-class full, rather than next to it. This is because we want the
collapse buttons to be hidden with the full texts, too.
Now we need to have some action when the user clicks one of those buttons, too:
$('.collapse').on('click', function(){
$(this).parent().slideUp().prev('.more').slideDown();
});
Now, this was easy: We start with the button element, move the focus to its parent() (which is the element that contains the full text) and tell jQuery to hide that element by sliding it up with slideUp().
Then we move the focus from the full-text container to its previous element with the css-class more, which is its expanding button that has been hidden when expanding the text. We slowly show that button again by calling slideDown().
Thats it :)
I've uploaded my example on jsBin.

Jquery toggle mobile menu (remove href javascript)

I'm trying to make a jQuery toggle menu for a mobile website for one of my clients. I'll have to tell you i'm not experienced in javascript and i justed started looking at it.
The current website is a Wordpress website so the menu structure is generated by WP.
Because this is generated by WP i need to use javascript to manipulate the data for adding the + - and > signs for toggleing and if no childeren to go directly to the page.
I use this javascript for adding the spans with the desired icon. I've managed so far.
http://jsfiddle.net/9Dvrr/9/
But there are still 2 problems i can't seem to figure out.
Remove the href from the "a" when the "li" has a "ul" child.
This should remove the links of the items so they will only toggle (not link) to navigate straight throug to the deepest level.
Currently the javascript is adding mutiple spans with the icons. I can't seem to figure out why
I'm stuggeling with this for a while now and was wondering if someone could help me with this.

In the jsfiddle you provided, you loop on the elements to add spans with a "+" or "-" sign inside, depending on the case. The thing is, the HTML you're starting with already has those spans in it, wich is why you're seeing some duplicates.
As you said you can't add those spans in the HTML because of your WP strucutre, I guess they come from a bad copy/paste you did while creating the jsfiddle. I removed them in the HTML and added a return false to prevent linking to another page when there is a ul inside the a tag.
http://jsfiddle.net/wzzGG/

Your first problem can be solved with the following:
$.each($('#menu-mobiel li'), function(i, value) {
var $this = $(this);
if ($this.has('ul').length > 0) {
$this.children('a').attr('href','javascript:');
}
Your second problem is a bit harder for me to understand. Do you only want one + for items with submenus, and one > for items with a link?

Completely Reload TinyMCE

I have been writing a CMS for a while now and am currently putting the last few touches on it. one of which includes using ajax to deliver a tinyMCE editor in a lightbox styled window.
when it is loaded, the first time it works perfectly, but when i do it the second time or more, the element names get messed up and it doesn't send data back, or display the current value in the TinyMCE window. When I use Chrome to inspect the element, I can see that the span that contains the previous tinyMCE window is still there.
I use document.body.removeChild to remove the div that is holding it. Does anyone have any ideas?
Addition:
when AJAX gets back from making the request (it has all the html code of what goes in the window), it creates a new div element and uses document.body.appendChild to add the element to the document and puts the html code into the div tag.
Then it travels through the new code and searches for the scripts in that area (of which one is the MCE initiator) and appends them to the head so they are executed.
if the user clicks cancel rather than save, it removes the div tag by using:
document.body.removeChild(document.getElementById("popupbox"));
which works fine,
however when i bring up popup and repopulate as said before, and inspect the elements there, there is still a span there which was created by TinyMCE and the naming has been changed (instead of being identified by 'content', it is now 8 for some reason) and there is no content in the editor region.
I have used:
tinyMCE.execCommand('mceRemoveControl',true,'mce{$Setting['name']}');
tinyMCE.editors[0].destroy();
but neither of them work. They return the tinymce window to a textarea, but the elements are still there.

Removing the editor as you described (using the correct tinymce editor id) before moving or removing the html element holding the tinymce iframe is a good choice. Where do you load your tinymce.js? If you deliver it using ajax i think it might be better to load it on the parent page(!). Some more code would be helpfull.
EDIT: I remember a situation where i had to remove a leftover span. Here is my code for this:
// remove leftover span
$('div .mceEditor').each(function(item){
if (typeof $(this).attr('style') !== "undefined" ){
$(this).removeAttr('style'); // entfernt "style: none";
}
else {
$(this).remove();
}
});