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.appendChild() an HTML element on click

I wanted to copy an entire row including its' siblings and contents on button click. When I click the button the element, it appears in the console but doesn't append to the page. This is my code:
It doesn't show any error messages. I've tried innerHTML/outerHTML or append() it doesn't work.
$(document).ready(function() {
$('#addSubFBtn').on('click', function() {
var itm = document.getElementById("trFb");
var wrapper = document.createElement('div');
var el = wrapper.appendChild(itm);
document.getElementById("tbFb").append(el);
console.log(el);
});
});

Seems like what you're trying to do is clone the item after you get it from your document. W3schools website explains how to accomplish this. Check out the link: https://www.w3schools.com/jsref/met_node_clonenode.asp
Once you clone the node, [appendchild] should work as intended

Not sure (as said without seeing related HTML) but i see flaw in your logic:
var itm = document.getElementById("trFb");
still exist on the document(so in the page) so you've to retrieve it before you want to add/move it to another place.
using .removeElement will return you removed element(or null if no element matche the selector) so correct script should be:
var itm=document.getElementById("trFb").parentNode.removeChild(document.getElementById("trFb"));
as shown here to remove element you've to use method on to parent element.
So you can add it to any other element existing.
For more specific use or element created in global JS variable (such an createElement not yet appended) you can see :document.createDocumentFragment(); as explained here https://developer.mozilla.org/en-US/docs/Web/API/Document/createDocumentFragment

Manipulating jQuery object without changing the html element

I have a variable with a jQuery object, for example:
var div = $('#div_element');
How can I manipulate ONLY the div variable, without changing the #div_element itself?
I want to do some edits on the div variable and to pass it as an argument to a plugin, like this:
var el = $('#div');
el.find(':first').remove();
$().popup(el); //I wrote this plugin myself
Actually I want to display popup containing the #div element (with removed the first "child"), but don't want to change the #div element itself.

Use clone to create a copy of the element.
var el = $('#div').clone();

You can use like
$().popup($("#div :not(:first-child)"));

Add an id to a dynamically created element

I'm trying to add an id to an element that I create dynamically using javascripts' document.createElement() method. Basically I want to create an iframe in my html document and at the same time give that newly created element an id.
Here's my code so far. I've figured out how to put the element in the DOM and all that, i just need the id.
function build(content){
var newIframe = document.createElement("iframe");
var newContent = document.createTextNode("Hello World!");
newIframe.appendChild(newContent);
var element = document.getElementById("container");
document.body.insertBefore(newIframe, element);
document.getElementsByTagName("iframe").id = "active";
};
As you can probably see, I have tried to give it an id at the very end. Problem is, it doesn't work.
So if anyone has any idea of what is wrong here, or an alternative way of doing what I want to do, please feel free to express yourself. Many thanks!

Just add an attribute (id is an attribute) to that element directly, like this:
var newIframe = document.createElement("iframe");
newIframe.id = 'active';
... although it looks quite strange to have id equal to active (too generic for a unique identifier).
Your current approach doesn't work because document.getElementsByTagName("iframe") returns a collection of elements - NodeList or HTMLCollection (it's browser-dependant). While you can assign a value to its id property, it won't do what you mean to. To make it work, you can adjust it this way:
document.getElementsByTagName("iframe")[0].id = "active";
... but, as shown above, there's a better way.

newIFrame.setAttribute("id", "something");

Moving the content of a DIV to another DIV with jQuery

http://www.frostjedi.com/terra/scripts/demo/jquery02.html
According to this link elements can be moved around by doing $('#container1').append($('#container2')). Unfortunately, it doesn't seem to be working for me. Any ideas?

See jsfiddle http://jsfiddle.net/Tu7Nc/1/
You must append not your div exactly, but your div's content(inner HTML) with Jquery's html() function.
HTML:
<div id="1">aaa</div>
<div id="2">bbb</div>​
Jquery:
$("#1").append($("#2").html());
Result:
aaabbb
bbb

It is best not to use html().
I ran into some issues due to html interpreting the contents as a string instead of a DOM node.
Use contents instead and your other scripts should not break due to broken references.
I needed to nest the contents of a DIV into a child of itself, here is how I did it.
example:
<div id="xy">
<span>contents</span>
</div>
<script>
contents = $("#xy").contents(); //reference the contents of id xy
$("#xy").append('<div class="test-class" />'); //create div with class test-class inside id xy
$("#xy").find(">.test-class").append(contents); //find direct child of xy with class test-class and move contents to new div
</script>
[EDIT]
The previous example works but here is a cleaner and more efficient example:
<script>
var content = $("#xy").contents(); //find element
var wrapper = $('<div style="border: 1px solid #000;"/>'); //create wrapper element
content.after(wrapper); //insert wrapper after found element
wrapper.append(content); //move element into wrapper
</script>

To move contents of a div (id=container2) to another div (id=container1) with jquery.
$('#container2').contents().appendTo('#container1');

You can also do:
var el1 = document.getElementById('container1');
var el2 = document.getElementById('container2');
if (el1 && el2) el1.appendChild(el2);
or as one statement, but not nearly as robust:
document.getElementById('container1').appendChild(document.getElementById('container2'));
Edit
On reflection (several years later…) it seems the intention is to move the content of one div to another. So the following does that in plain JS:
var el1 = document.getElementById('container1');
var el2 = document.getElementById('container2');
if (el1 && el2) {
while (el2.firstChild) el1.appendChild(el2.firstChild);
}
// Remove el2 if required
el2.parentNode.removeChild(el2);
This has the benefit of retaining any dynamically added listeners on descendants of el2 that solutions using innerHTML will strip away.

$('#container1').append($('#container2').html())

Well, this one could be an alternative if you want to Append:
document.getElementById("div2").innerHTML=document.getElementById("div2").innerHTML+document.getElementById("div1").innerHTML
if you wanted to rewrite contents:
document.getElementById("div2").innerHTML=document.getElementById("div1").innerHTML

I suggest a general approach with a function and jQuery:
function MoveContent(destId, srcId) {
$('#' + destId).append($('#' + srcId).contents().detach());
}
Content of a detached source node is appended to a destination node with call:
MoveContent('dest','src');
The first parameter is an id of a new parent node (destination), the second is an id of an old parent node (source).
Please see an example at: http://jsfiddle.net/dukrjzne/3/

How do I insert a block of html after a block that I have just rendered on the DOM

I am building a block of nested divs around a specific element on the client. I am using jQuery's .wrap() initially to get the first part of the block which is working fine. But now I want to attach the ending block after the element I am wrapping and I am finding I can't attach it to anything because it is all being created at the same time. I tried using insertAfter() but I don't want it to be a sibling of the element I am wrapping, I want it to come after it's parent.
Here is my code:
$(document).ready(function() {
buildShadows('#section');
});
function buildShadows(element){
$(element).wrap("<div class='section_shadow_wrapper'><div class='section_shadow_curve'><div class='section_shadow_outer'><div class='section_shadow_inner_left'><div class='section_shadow_inner_right'>");
$("<div class='section_shadow_bottom_left'><div class='section_test_bottom_right'>").insertAfter(element);
}
What I am trying to do is append the first element of the second part (section_shadow_bottom_left) as a sibling of 'section_shadow_inner_right' but after 'element'
Any help would be appreciated.
Thanks.

You should be able to just traverse up to the new parent you just created.
Have you tried this?
function buildShadows(element){
$(element).wrap('<div class="section_shadow_wrapper clearfix"><div class="section_shadow_curve"><div class="section_shadow_outer"><div class="section_shadow_inner_left"><div class="section_shadow_inner_right">')
.parent().after('<div class="section_shadow_bottom_left"><div class="section_test_bottom_right">');
}

Try traversing to the next sibling of the original element and using .insertBefore() on it.
var nextsibling = $(element).next();
//Wrap code
$("<div class='section_shadow_bottom_left'><div class='section_test_bottom_right'>").insertBefore(nextsibling);