I'm sure that my FIL has done something on key use by Mozart (as Mozart is one of his specialities) - I think that you really get into this a lot when you look at Listz and Strauss etc.
Perfect pitch - I suppose I would say that if you don't know the pitch of notes, its being able to hear a piece of music then, possibly several days later, sing it at the 'correct' pitch (as that is where it 'fits')
Had experience at choir last night. Concert coming up. One of the movements has a long unaccompanied bit to start. Choir, particularly tenors, goes flat. I can keep in tune (with what it should be), and, indeed, find it difficult not to. Unfortunately, this sounds abysmal as I am at times about a 1/4 tone out with the rest of the choir (100+) .
The other choir I sing with never goes flat. If anything, it has a tendency to go a little sharp, although not badly. This choir is smaller, and does lots of unaccompanied stuff, but also does accompanied and with small orchestras etc.
I know music does run in families, although to a greater and lesser extent. That's why we've started Ds early on the violin given that he has expressed an interest in it - and string playing should run in his blood (hopefully)