will a 2006 Pontiac grand prix base model transmission fit in a 2007 Pontiac grand prix base model
I personally don't see any issues in swapping an Auto Trans from the 2006 and putting it into a 2007 GP. The 2007 car didn't have any significant changes in design, transmission, engine, etc (It was a carryover from 2006, from what I know). Plus, you're going from base model to base model. If you were switching from a GTP to a Base, there might be an issue...otherwise, I'd say you're good to go.
Yes. The parts in the 2004-2008 should be interchangeable. That was the seventh and last generation.