Both can’t be from the same state.
Yes and no. It does make it less likely that Giuliani would be Trump's running mate, but I know they are fairly close. Neither the constitution or the electoral college prevent a presidential candidate from choosing a VP from the same state. But in the case of a close election it could complicate matters in the electoral college. So as far as I know it has never been done, but it actually is possible and not against the law.