so lets say pence becomes president
and the house refuses to approve a vice president
does that mean the senate has no president? and the VP couldnt serve as a tie breaker if the senate is 50-50?
In theory, yes. Although I would assume since this is Pence, they would let Pence pick his VP.
If Pence was the one who dies, and Trump tried to appoint one for the Supreme Court so to speak, Pelosi could block it.