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: 
I was wondering this myself recently. Obviously the DHTML doesn't make sense, but the basic syntactic sugar and things are rumored to work.

* There is this [jQuery on XUL](http://groups.google.com/group/jquery-dev/browse_thread/thread/4545040bf26c6eea?pli=1) discussion from the jQuery group which indicates that it loads up with some exceptions.
* Also see this slightly more recent blog post about [jQuery and DHTML in XUL](http://digitalmihailo.blogspot.com/2008/05/jquery-and-dynamic-html-in-xul.html). That person is going after the HTML within the XUL which is not exactly what you need but he does have good information.
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.