The only records I can really see being broken is the steals in one game. Other than that, a lot of the records are just out of reach for the game these days.
Probably not. Teams get dismantled too quickly these days and the salary cap keeps players on the move. The Celtics of the 60s were able to put together extremely talented teams (like the 1961 championship team featuring nine Hall of Famers) and keep them together year after year.