No. If a balk occurs with the bases loaded all three runners advance one base, however, the batter does not advance to first base.
Yes, if the catcher drops the ball
That is called a "Grand Slam".
He can be called out for purposely getting hit.
the batter is out and the run doesn't count
No. When a batter is hit by a pitch, the ball is dead and no runners may advance. However, if the bases were loaded, then all runners are forced to advance and the runner from third would score.
Yes. He can be called out because he will be outside of the line and he can be called out.
Yes, the batter that walks in a run due to the bases being loaded will receive credit for a RBI.
Throw the ball back to the pitcher. A batter can not advance on a dropped third if first base is occupied.