Look for parking sites like ICON Parking you can reserve parking spaces a few months in advance.
I'm not sure but you can book online before you go
Sorry, don't know. Parking is so expensive in NYC that we usually park at Secaucus, NJ and take the train to the city, making it an adventure for the family.
You should be able to, Check Groupon as well
Sorry. I do not know. I stayed at an hotel very closed to the theater.
Thanks! Your answer is awaiting moderation.