Question: I know its possible to integrate jQuery within Firefox addons, but are we able to manipulate (animate, move, adjust transparency, etc) XUL elements themselves?

From what I understand, the Firefox addon can use jQuery to manipulate HTML/DOM elements, but not sure about XUL elements.

Answer: 
XUL and HTML actually deal with opacity the exact same way, and it is jQuery that incorrectly detects what the browser can do. jQuery thinks it's in a different browser when it's living inside XUL, and so opacity effects are handled differently - by jQuery. Since it IS in Firefox, and it should deal with opacity normally, you can override this like so:

jQuery.support.opacity = true

Do this right after jQuery is loaded.

There is probably a whole category of similar fixes that can be post-applied to jQuery to make it behave better, but I haven't looked in to it.
Unfortunately, jQuery fails to initialize in XUL because of the HTML-specific functions like `document.body` that exist for HTML pages only. However there is a special branch called [jQuery-xul](https://github.com/ilyakharlamov/jquery-xul) that it optimized for use in FireFox extensions. I have checked, it works fine.