Does the vice president also serve as the president

Technically no, but if anything were to happen to the president then the vice would be a temporary replacement. 

The VP has very little legal power that is listed in the constitution, but I would bet he has large amounts of power as a politician.

He is a helper for the president and serves as diplomat

If the senate is in a 50-50 deadlock, the senate breaks the vote. On that note, socially not legally, he serves as a connection between president and congress leaders. He acts as the "president of congress" because he works with them a lot, but that is no where listed in the constitution.

Of course, VP's roles can change as history goes.