Please Help Me Clear These Up

[BigMurr]

First time poster, long time reader. I am going into coaching this year and wanted to clear up a few things I have taken note of so far in the MLB games I've watched this season.... I know MLB rules don't = the rules I will be coaching under, but for the most part they are common.

#1 - I saw an umpire call a "ball" twice on a pitcher for licking his fingers. The commentator mentioned he can't do this on the mound? Is this correct? Can he do it off the mound? I think the umpire was named Diaz.

#2 - Can an infield fly be called on a bunt that pops up high into the air?

#3 - Why do they always show the side TV angle on half-swings? Is it true that the bat has to cross the plate to be a strike on a check swing? I can't find a rule reference for this. What happens if a guy is way at the back of the box?

#4 - Does the pitcher have to have his entire foot on the pitching rubber or just part of it?

#5 - How far is the batters box away from the plate?

#6 - If a player hits the ball twice with his bat, is he out? Is it foul?

#7 - What happens if the runner runs out of that first baseline lane to avoid a first baseman attemting to catch an errant throw... but then the batter gets hit by the ball? Is it interference on the batter?

#8 - What is the process for appeals? It is common to see the pitcher set, step off, and throw to the base... but I can't find a reference for this either.

#9 - Do teams have to have a 1st base and 3rd base coach at all times?

Thanks a lot for some help. I want to make sure I am teaching my guys the correct rules.

I really appreciate any help.