I'm not 100% certain, but I think Zarek was addressed (with some irony) as "Mr. Vice-President" in the previous episode where he & Roslin were about to be executed.
Could be. That had been the impression I had since the election last season. I honestly don't recall that from one of the more recent episodes.
I think that Zarek's being held in a detention center for four months for refusing to cooperate with the Cylons might have resulted in his removal from office.
As for who's President, we'll have to see. I think they'll hold another election after they finish picking up all the pieces of their existence -and weeding out the collaborators.