1. Yes, that's just what it means.
2. I'd say 'on the stage' or 'on stage' - both are set adverbial phrases, and don't refer to any one stage in particular.
You could say 'This also applies to' here. It does sound a little awkward, though, because it it's a relatively formal expression, generally used to refer back to a more complex phrase or idea than simply 'She likes'. Your second version (.. as well as..) sounds more natural.