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jQuery chosen scroll issue, element which contains the chosen doesn't scroll

I am facing some issues with the jQuery Chosen plugin. Here are some screenshots:
The focused Users input is a jQuery Chosen select input within a tab in a Bootstrap dialog (but this doesn't matter anyway). As you can see the scroll of the Chosen's ul.chosen-results didn't reach the bottom here.
Now if I scroll down the results:
I reach the bottom of ul.chosen-results, but if scroll with the mouse wheel down further from this point on, the rightmost scroll doesn't scroll down.
But I would like the other scroll to go down too from that point on while scrolling down ul.chosen-results with the bottom scroll of ul.chosen-results reached, to achieve this:
See that the rightmost scrollbar is down here too. This is what I want to reach while scrolling on ul.chosen-results. Does Chosen somehow inhibit the scroll event propagation when scrolling ul.chosen-results?
Can I achieve what I want? How?
Thanks for the attention!

In the not minified js plugin file
find following code
high_top = this.result_highlight.position().top + this.search_results.scrollTop();
and replace it by this.
high_top = this.result_highlight.position().top;
This issues has been addressed here another possible fix is to update to jQuery 2.2.1

How to prevent people from scrolling using mouse wheel press our touch dragging?

In HTML/CSS/JS, there is one thing I am having trouble figuring out:
How to prevent people from scrolling an element using the mouse wheel press (i.e. hold down the mouse wheel and drag, or click the mousewheel, drag, click the mouse wheel again) and how to do the same when people try to drag the elements around on a touch-device.
This is something I stumble upon, amongst other places, when trying to make a hamburger-style menu.
Setting an element's CSS to overflow: hidden will hide the scroll bars, but using above two methods, it is still easy to scroll through them.
Until now, the only 'solution' I found was to make a second element, and position it on top of the element that should not be scrollable. But this hardly seems like a perfect solution to me.
How can these events be captured using JavaScript?
How can, on, for instance, this page, scrolling horizontally and vertically be blocked when the menu is open?

If you create a jsfiddle, we can give a better solution. If you are OK with jquery, I can give some solution for your second point "How can, on, for instance, this page, scrolling horizontally and vertically be blocked when the menu is open?".
First you need to create one simple class like below.
.overhidden
{
overflow:hidden !important;
}
Next, we need to apply this class when you press the menu icon on your screen. Also we need to remove if they click again for closing. It is easy to do in jquery like below.
$(document).ready(function(){
$('#hamburger').click(function(){
$('body').toggleClass('overhidden');
});
});

Is there a search/find event in browsers?

I'm in the middle of building a not scrollable, fixed layout website, but as usual, non conventional websites tend to have shortages. There is a scrollable news element in the page, which scrolls a div container's div childs up and down by the mousewheel. The problem arises, when someone tries to search in the page, pressing CTRL+F and the content is out of the viewport (not scrolled into view). Is there any common event, which handles the find/search inside browsers?

Im not completely certain about this, but I dont think DOM has any events that fire when a uses searches and that it a browser function that you can not hook on.
http://en.wikipedia.org/wiki/DOM_events

Prevent snapback to original position in iScroll4

I'm using iScroll4 to make a certain element scrollable in my webpage but it snaps back to the original position once you release the mouse/touch. How do I make it stay instead?

I think that I have figured out why this happens. I had iscroll4 working in a Phonegap app that I was building, and then broke it after changing some CSS. At the time, I didn't realize what I had done and I spent a long time hunting for a Javascript solution.
Finally, I noticed that when I tested it in a browser, there was a scrollbar for the list where I was using iscroll4. And when I tried to scroll, the scrollbar thumb changed size. That is why it was snapping back. The browser made the wrapper div big enough to hold the entire list, so whenever I tried to scroll, there was no hidden data so I triggered the pull-up event and then the browser resized the div.
I had to change the CSS to include overflow:hidden and it started to work again. I tried overflow:hidden on the ul tag and the scroller div but that didn't work. It has to be on the wrapper div.

How to prevent mouse scrolling outside hovered element?

I have a div which is set to overflow:scroll;. I get scrollbars which is what I want. However when scrolling the div with the mousewheel it scrolls the rest of the page when it reaches the top or bottom of the div's content.
How can I scroll only the div or the entire page based on what's hovered ?

First I don't think you can override the scroll event. So here is what I would do. I don't know jquery but here is some straight javascript.
document.getElementById('scrollDiv').onmouseover=function(){
document.getElementByTagName('body')[0].style.overflow='hidden';
}
document.getElementById('scrollDiv').onmouseout=function(){
document.getElementByTagName('body')[0].style.overflow='';
}
Obviously you could tweak this a little, but this is the basic idea. Also, if you need to you could do other test cases. Like if the div has focus then do the same thing. Depends on your setup.

You could test the mouse position and cancel the scroll events for the document if the mouse is within the bounds of the div.

In this case, I think you'll have to override the default onscroll event for the body. In your handler, you'll need to manually scroll the div's contents.