This is more a comment rather than a question.
I noticed that with newer version of Animate (2014.1.1 I am using), when publishing Animate does not export the core jQuery.js file it used to, and instead now it adds a single Edge.5.0.1.js
So may I assume that exporting jQuery mobile JS file is no longer needed?
I found some trouble adapting some already made Edge Animate files to the new situation, as I used to add some other external JS files (like jQueryUI) that rely on jQuery, and now they don't work unless I add jQuery library manually. Is that correct? Is it the best way to proceed now?
Yes you are correct in your discovery.
hope this helps