JQuery Mobile requires JQuery as a prerequisite.
You can't "exchange" the files. You need them both, and you nedd to load JQuery first.
You can make use of JQuery features in your Javascript. In fact, you should, rather than using DOM manipulation functions directly.
JQuery Mobile is not compatible with JQuery UI, though some people have gotten some JQuery UI widgets to work with JQuery Mobile. I mention this only because - although it's not a part of JQuery - JQuery UI gets some considerable coverage in many books on JQuery.