Is the batter out if the batter hits a ball and throws his bat and the bat hits the catcher and as a result the catcher is unable to field a throw for a play at the plate?

Answer 1

Yes. If at any point in a game, the batter or baserunner interferes with the fielder, he is an automatic out. If he impedes the throw to get out another runner, the other runner is out as well. For instance, on a double play, if the runner going to second is already out by force at 2nd, and he plows into the short stop trying to throw the other runner out at first, the runner going to first is also out. The baserunner must always slide or otherwise avoid excessive contact with the fielder on a double play.