That's true, Nancy could block the VP nomination. I thought it was just the Senate, but it's both houses have to confirm.
That would be the Democrats subverting the twenty-fifth amendment. Some Democrats threatened the same thing when Spiro Agnew resigned.
Yes, they could block the VP nominee from being confirmed, but it’s possible the “Federal Vacancies Reform Act of 1998” could come into play. That act authorizes the President to fill a vacancy with an “acting” officer pending confirmation of the permanent nominee. I’m not sure if that would apply to the VP, but it seems like you can at least make the argument that it does from the way it is worded.