Does a batter have to warm up in the on deck circle?

Answer 1

Technically they are not allowed to be outside the circle, but every on deck player usually does so. I have personally seen Derek Jeter, almost behind home-plate .near the stands to get a better look at the pitches. The umpires will allow this until it interferes with the flow of the game, then they will not allow it anymore.

Answer 2

No. Many times you will see someone warming up in the on-deck circle and then at the last minute a manager will make a substitution and that new player will go directly from the bench to the plate. I doubt, however, that you will ever see a scheduled player not warm up and swing before his at-bat.