No he is not out. Hitting the rubber is like hitting the ground. He would have to throw out the batter, runner at first base.
yes.
Yes almost all do
No. Remember there are left handed pitchers and right handed pitchers. Almost every umpire will declare a right handed pitcher to have balked if his foot doesn't disengage from the rubber when he throws to first. A left handed pitcher simply steps and throws to first. His back foot usually never disengages from the rubber. To over simplify - a pitcher is called for a balk when the umpire judges the pitcher to have deceived the runner in some way. So, anytime a baulk is called, an umpire made a judgement call.
The DH then proceeds to first base.
Pitchers throw harder... by a little bit.
The strike zone
No they do not you have to throw the ball to a base to get an out.
Yes. But he has to be careful not to balk.
throw them out
The pitching distance is 40 feet from home plate to the back of the pitching rubber. For 18U Gold and collegiate softball the pitchers mound is 43 feet away. This is because pitchers throwing at these levels throw much faster than those at the lower levels, making it a lot harder for batters to identify pitches.
ITS OVER 9000mph!!!!!!!!!!!!!!