Is there a rule in the Fed about the batter throwing the bat after he swings.

Yes There is!
 

3-3-1b
A coach, player, substitute, attendant or other bench personnel shall not: carelessly throw a bat:

PENALTY: At the end of playing action, the umpire shall issue a warning to the coach of the team involved and the next offender on that team shall be ejected...

3-3-1m
.... shall not: deliberately throw a bat, helmet, etc.

PENALTY: The umpire shall eject the offender from the game. Failure to comply shall result in game being forfeited...