Hello Angel,
the problem comes from your template that adds its own sets of Mootools and jQuery files. Although it helps the template to keep control over the way libraries are loaded, it is a nightmare once other components add there own libraries... The one thing I would suggest here, if you cannot disable MooTools and jQuery from your template, is to add the line:to the list of remaining scripts to strip.

You need to look at your source code once you have made modifications to make sure they occur as expected.
I can see that the line I asked you to add is still there for instance.
Do you reall need jQuery UI? Unless you are replacing jQuery UI for a component, you don't need it here.
As far as knowing if you have the right version of jQuery, you have to check every component that uses jQuery to make sure they work with that version.