Yesterday I used jQuery UI for the first time and I think I'm going to switch from Dojo to jQuery UI.
I noticed that jQuery UI comes with a set of CSS themes.
Yes, you can use them wherever you feel like, just specify the classes you're interested in using.
JQueryUI doesn't make a habit of changing its class names, so that shouldn't be much of a concern.
Not much more to say except to make sure JQueryUI already handles a particular styling you're looking for before you go to code your own.
Can I use them in my pages for non-jQuery related stuff?
Yes you can. They are just CSS / images that follow particular naming conventions.
Are the CSS class names subject to frequent changes?
Probably not. I don't see the UI team changing them in any big way without prior announcement of the changes and reasons for the changes.
Are there any other things and/or best practices I should be aware of?
Have a look at themeroller if you haven't already - it's the easiest way to build themes for your UI components.