1. The batter is out if, in the umpire’s judgment, the outfielder made the catch while still legally on the playing field and held the ball securely after tumbling into the stands.  The runner at second is entitled to advance one base after the play.  Rules 2.00—Catch, 6.05a, 7.04c

2. If the pitch is not thrown, the balk is enforced and the count remains the same.  The runner just moves up a base.  Unless the following occurs, the batter reaches first base on a hit, base on balls, error, or otherwise AND all runners move at least one base, the balk is not enforced.  Rule 8.05

3. The lineup in the plate umpire’s possession is the official batting order.  Since that order was followed, the appeal is disregarded.  Rule 4.01c

4. No.  In this case, although the ball was under the fielder’s hand, it could not reasonably be considered to be securely held by hand or glove because it was actually entrapped by the uniform.  Rule 2.00-Tag, Catch

5. Although the batter winds up with just a single instead of a triple, all three runs count.  The third out on the appeal did not occur until after the three runners had crosses the plate and consequently the scores are legal.  Rules 7.02, 7.10b, 4.09a

6. The runner is safe because the catcher’s interference causes a balk to be called on the pitcher, entitling each runner to advance one base, while the batter is awarded first base on the interference.  Rule 7.07

7. He’s out.  When a base runner collides with an umpire, this does not constitute interference and the ball remains in play.  Rule 2.00—Interference-c

8. No stretch is required when pitching from the set position  However, he must come to a stop after bringing his hands together.  If he doesn’t, it is a balk.  Rules 8.01b, 8.05m

9. False.  In situations where the catcher has to make a throw, the batter is better off staying in the batter’s box but that does not immunize him from being called for interference.  The catcher expects the batter to be in the batter’s box and usually plans his throws around the batter.  On this type of play, any intentional or unusual motion in the batter’s box or stepping out of it can cause interference. 

10. No.  The ball remains in play and runners can advance at their own risk.  In such a case, the batter is out only if, in the umpire’s judgment, he steps out of the box or makes some other movement to hinder the catcher’s play.  Rule 6.06c