What secondary skill would it fit into?
If none, what category amd characteristic would match ot the most?
And also, what difficulties would make credible and realistic?

That is a hard one. Personally I would put it as a form of "art" and be an opposed check, against a Notice check ( to see your mouth moving, to hear the difference between what your imitating, etc). If you don't like Art it could be under Music , as that it's sort of but completely different from singing.

Depending on what they are trying to do it might be assisted by a Slight of Hand check to create a distraction.

Determining its credibility would be the amount you beat them by, if you beat them by 120 they believe it completely, but if you beat them by 20 they would be slightly suspicious, but not too curious.

I'd use Disguise for this one.

I'd use Disguise for this one, since you're disguising your voice and/or its provenience.