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JS : How to get notified after insertBefore()?

Is there a way to get notified, after inserting an element into the DOM with insertBefore(), when this element becomes actually visible/available to user ? Especially to start applying CSS transforms on it ?
Complete problem
Forgive me if this question is recurrent, I didn't find a suitable answer so far. I'm trying to implement a custom popup dialog system on a website of my own, similar to SweetAlert or some other products.
I would like to apply some special effects when this popup shows up, such as a progressive darkening of the background, as well as a slow vertical motion on the box itself.
To achieve all of this, I spawn one big, fixed div element covering the whole screen (the background) and containing the popup box. When I need it, I first insert this element as body's first child, tagging it with a special invisible class. Once inserted, I remove this invisible class from the element and let the CSS rules do the magic.
The problem is that even if removed the class after having inserted this element, this one will be rendered only when the Javascript function leaves, hence directly in its final state.
When doing this on a complete initial page, the load event helps. I now would like to do the same on an existing page.
As always, I'm interested on both solutions to this (potentially XY) problem: if there's a better way to do it, I'll be happy to discover it, but I'm still interested in solving this particular situation anyway.
Thanks in advance to everyone.
EDIT: currently performing tests on Firefox 82.0.2

Thanks to comments above, here's a valid solution to both exposed problems:
"Mutation Observer", as well as former "Mutation Events" (now deprecated) are the best way to get notified when something is inserted. It won't help with animations issues, though, because it's still not guaranteed to be rendered yet at this time ;
Rather than applying a class then another to perform a transition, it's better to define a regular animation using #keyframes that plays only once. It's guaranteed to be played when the object appears, by definition.
Many thanks to "Pomax", F4st3r and epascarello for their help.

Understanding JavaScript events and applying jQuery events/plugins?

I have a bunch of jQuery functions that use the .on event because I want to prevent reapplying the event to the same element.
However some people created plugins (e.g. Owl Carousel) and I don't know how to prevent this event from reapplying.
Currently I am using the plugin as following:
HTML:
<div class="init-owl"></div>
JS:
$('.init-owl').owlCarrousel();
$('.init-owl').removeClass('init-owl');
Whenever a second element gets loaded in the page using e.g. AJAX, I want to only apply the event to the newly added element.
Question: What I dont understand is how the event stays stuck to the DOM?
To better grip what is happening, I was wondering how an event in general gets connected to the DOM?
Is there a better way to prevent events applying to the same DOM elements?
If I wish to write my own plugins, I would need to know how javascript works, right?

Question: What I dont understand is how the event stays stuck to the DOM?
Once an event is bound to an object, it gets removed when the object gets garbaged collected. So if a DOM element is really gone and there are no references to it, then the event will get swept up as well.
To better grip what is happening, I was wondering how an event in general gets connected to the DOM?
I'm not sure how far you want to dive into this. Maybe it would help if you stop thinking about the DOM and events and look more at just regular events bound to objects. Basically an object does something, or something is done to it and some underlying code (in the browser's code in this case) triggers an event on that object. The implementations between browsers may differ, but basically you will have a key or string (the event name) that maps to a collection of functions. When you add an event listener, you add another function to this collection. Then when something triggers that event, it iterates through the functions and executes them. That's a real basic explanation, but I hope it makes things a little more clear.
Is there a better way to prevent events applying to the same DOM elements?
Make sure you don't add the events again by writing better code. I don't believe you can dive down into an element and look to see if it has events bound to it. You can however change your jQuery selector to only target newly added elements. If you have to, mark the elements that you have added events to with a class or something. Then you could target your elements by doing $('.init-owl:not(.already-bound)'). There is a better solution to your problem, I can assure you, but we might need more context and code to see a better way to help you.
EDIT:
You can look into jQuery's off() function to remove events. That may help you too.

How to fire a DOM event with YUI3

I've encountered an annoying issue while working on YUI.
I have a main area and a navigation block. The elements in the main area can be activated with a direct click or by clicking an element in the navigation block that triggers the appropriate element in the main area.
As it turns out, triggering a click event programmatically in YUI isn't as simple as I thought it might be. Looking at the documentation I found pleanty of information on how to attach and delegate events but not how to call one.
I found this question, but it deals with creating a new custom event and not calling an existing one.
All other similar questions are answered with using .simulate(), but this is actually not the best option for compatability reasons and it's also not recommended by YAHOO itself for client-side use http://yuilibrary.com/yui/docs/event/simulate.html#faking. EDIT: After re-reading the section I realized the warning is irrelevant for the subject of this question.
I found a solution by calling the click() command in the node's DOM element, but this is really a last resort and I would like to know if there's a more "clean" way to do it through YUI.
Here is an example of what I'm doing now: http://jsfiddle.net/3fso2dg8/
In the example, the second button is triggering the click event of the first button by using the DOM element
Y.one('#clickme')._node.click();
CONCLUSIONS
After more fiddling with the code I came to realize simulate() is the preferred option in most cases, but not all.
The YUI vesrion I'm required to work with (3.14) has a known issue on simulating a click event in IE9 and above. Since - for other technical reasons - I cannot upgrade to whatever version this issue was fixed and I need to keep a multi-platform compatibility, my original solution is still the best option. Anyone else that uses YUI components that don't respond well on IE, maybe you stumbled upon the same issue so this is one way to solve it.

After looking for exactly the same functionality I just used simulate in user-facing code - where It would just mimic clicking with no return method etc. (simple submit button or choose fil trigger).
When I would needed "complex" functionality I would just add a class or new ID and add new delegate or "on" method in my code - following the: "If a function needs to respond to user action or be called programmatically, it should be written accordingly and called directly in the latter case." prinsipp.
So to summarize - I use simulate for very simple effects with no callbacks or other "advanced" stuff and (sadly) duplicate other delegate/on elements where simulating would be tricky...
Had also looked into your method (._node.click();) and I can't see no obvious difference comparing to simulate()...

is it possible to view one html element twice on the same page, or must I create a duplicate?

I am creating a site that allows viewing and editing the contents of the 'src-div' contents within the 'edit-div.' I am not editing the src-div directly, because its thumbnailed using css zoom property.
I have considered using knockout.js to bind both elements to an observable. Currently, I have implemented the feature with jquery .html() function: simply set edit-div innerhtml to src-div innerhtml on 'select', and reverse the process after changes are made to edit-div to update the src-div.
I am wondering if I really need 2 divs here, or if there is some way to actually view the same element twice on a page, and any changes made will automatically reflect in both 'views,' elimiating the need to copy innerhtml property back and forth between two elements.
essentially, this is like a mirror effect, without the flip.
the closest thing I found so far is:
http://developer.apple.com/library/safari/#documentation/InternetWeb/Conceptual/SafariVisualEffectsProgGuide/Reflections/Reflections.html
Any recommended practices for performing this task are appreciated.

(Almost) everything you see on a page has a counterpart in the DOM. Everything in the DOM gets exactly rendered one time (apart from pseudo-classes). And every node in the DOM can only have one parent (no exclusions).
Unfortunately you'll have to clone the specific node and add changes to both, as there is no copy & translate mechanism in the current CSS documentation.

If you're using jquery you can use one div and "clone" it. You can read this for more information.
http://api.jquery.com/clone/
If you set the class of the div to the same thing, you can have changes propagated to both. Then you can apply .addClass to the second div to apply a "reflected" affect (if that's your final goal).

jquery event for on render an element

I am trying to do all dom manipulations off screen and then make it visible. Which works, except now I have the situation where I am trying to do it with a form which I want to focus on the first input text upon rendering it on the browser.
Something like: myForm.prependTo(myDiv).show().find('input:first').focus();
Problem is that the focus is being called before the form has finished rendering which is causing the lovely error 'Can't move focus to the control because it is invisible, not enabled, or of a type that does not accept the focus'
How do other web developers handle the similiar situation of manipulating elements off screen and then making it visible? I wish jQuery had something like myForm.prependTo(myDiv, function() { /* on render code here */ })
I know one way of doing it is setting a timeout and when it fires I put focus on the input, but I feel like that's not really the cleanest way to do things. I know the iframe has an onload event, so I'm curious if people usually draw their elements in some hidden iframe and listen for its load event to know when the element has finished rendering? If so could you point me to an example of doing this?

myForm.prependTo(myDiv).show(function(e){
$(this).find('input:first').focus();
});​

I know I'm 7 years late, but I had a similar problem, which I solved by putting the stuff I needed to happen after the render in a ready handler.
I had a restore function that worked, but there was zero or near zero visual feedback that the element had been restored.
I tried emptying the element first. It still worked, but still had zero visual feedback.
$("#someSelector").empty();
restore();
Then I discovered ready() happens after the rendering; so I changed it to something like....
$("#someSelector").empty().ready(function() {
restore();
});
Now the restore() doesn't happen until after the empty() action RENDERS. This means my element APPEARS to empty out and then refill (it always did, but now the user can see it happen).
I found this solution somehow a few days ago for a different problem with some vague search that I can't remember. Then I needed it again but couldn't exactly remember what I did. Now my searches included the word "jquery" and "render" and lead me here.
I ended up going thru my code to find out what I did, and I thought it might be a good idea to post it here in case other people stumble on this post and actually need to execute something AFTER rendering happens.
Cheers.