I believe the answer to your first question is no per se. That is not to say the two of you could not get back to back awards and ask at the hotel to keep the same room.

The 3-night rule has been enforced in the past, but is usually waived on weekends, resort properties, or if you don't have three nights. (Odd as it seems, Hyatt has been tighter on us during the week at city hotels).