Can they do car registration for cars brought in from out-of-state?

Yes if transfer to California

Yes I think so, call or just go by.

I just got my Mercedes Registration at auto club it was from AZ they are open till 5 mon to fri n sat till 2

I believe they can do all types of DMV registration services as long everything's in order. Meaning as long as there's no holds/warrants/pending situations. However, I'd call AAA prior if there's anything you'd consider questionable about your situation.