#2
Possible. Probably not worth it. You'd see them, if you didn't use an opaque paint.

If you're dong it just for looks, don't bother. I'm not sure whether you'd need to re-jigger the control cavity itself, but that's just silliness.
#3
Well if you absolutely had to, you could totally re-do the control cavity and stuff. Just route the control cavity into an easy, simple shape and plug it with a block of wood made to fit it, then plug the pots' mounting holes with dowels sanded flush to the top of the body. Then you could either strip and re-paint the entire guitar (you'll have to use an opaque finish--no staining allowed at this point) or you could spot-refinish the bare areas and pray that the new paint is a perfect match to the existing paint (and it probably won't be). If the age of the guitar is significant, then stripping and refinishing it will completely alter its tone (I speak from personal experience).

It's a lot of work for what is, IMHO, little gain.