6. I see RapidGallery is based on jQuery. May I use it with Mootools-based templates/script/extensions. And may I use it with other jQuery-based templates/scripts/extensions?

Of course you can, don't worry about that. RapidGallery is designed to be conflictless with other javascript libraries and/or extensions.

If you already have jQuery, then RapidGallery will detect it and it won't be loaded twice. In some cases, some skins may require a specific jquery version to work, in such rare cases RapidGallery will load required version without causing conflicts and without overriding your current jquery loaded version.