Richvee

Once he steps off the rubber, he's an infielder. If I'm reading this right, he steps off the rubber, and then as he turns to 2B the pivot foot moves back and contacts the rubber? I've got a legal disengagement and an out.

If he makes a legitimate attempt to advance to second, it doesn't matter if he's in fair or foul territory.  It's the act of starting towards 2nd that must be judged. Keep in mind simply turning to the left after over running 1st is not an attempt to advance.

Yes. R3's run counts. As long as R3 crossed the plate before the appeal at 2nd on R2.  R2 is out on appeal. This is NOT a force play. It is a TIME play. 

In FED, the catcher, first baseman, or anyone else cannot hinder the progress of the runner. "In the act of fielding the ball" is NOT an exception to obstruction in FED.
Here's a case play regarding your play at 1st scenario.
8.3.2 SITUATION K:
F6 fields a ground ball and throws to F3 in attempt to retire B1 at first. The ball is thrown wide. As F3 lunges towards the ball, F3 collides with B1, knocking him to the ground prior to possessing the ball (a) while the runner is short of first base
RULING: (a) Obstruction;
 
 

Did it hinder anyone's attempt at making the catch? If so, INT. If not, and unintentional, foul.

Properly and legally equipped = No jewelry, (medical and religious necklaces/bracelets taped down), Legal bats  (BBCOR), and helmets free of cracks, without mirror like finishes.  Male Catchers only must have a protective cup, not every player.
ART. 3 . . . The catcher shall wear, in addition to a head protector, a mask with a throat protector, body protector, protective cup (male only), and baseball protective shin guards.
ART. 4 . . . The catcher's helmet and mask combination shall meet the NOCSAE standard. Any helmet or helmet and mask combination shall have full ear protection (dual ear flaps). A throat protector, which is either a part of or attached to the catcher's mask, is mandatory. A throat protector shall adequately cover the throat. The commercially manufactured catcher's head, face and throat protection may be a one-piece or multi-piece design. While in a crouch position, any non-adult warming up a pitcher at any location shall wear a head protector, a mask with a throat protector and a protective cup (male only).
 

Softball may be different, in baseball, the base is not a safe haven once the batter/runner puts the ball in play. If the runner, even if on the base, is tagged, AND THEN the fielder steps on 1st, (or tags the batter/runner before reaching first) it's a double play. However, if the runner is standing on first, and the fielder steps on the base first, and then tags the runner who is still on the base, the batter is out, the runner is safe since the force was removed when the fielder stepped on first to retire the batter/runner.

It is indeed batter INT. The batter is out only if there are 2 outs. Otherwise, the runner is called out for the batter's interference.

no run. Still a force regardless of if the runner or the base is tagged. 

For the windup position in most high school games which use FED rules, from the windup, the pitcher's free foot must be on or behind the rubber as you were told. This correct and is a FED rule. I can't get into the "whys"...FED has many rules that differ from OBR for whatever reason.
 
The main reason I see for this rule, is FED does not allow a throw to a base from the windup position. When a pitcher has his free foot in front of the rubber, it cannot be distinguished immediately  if he is in  a set or windup position, therefore, we can't tell if a throw to a base from that position is legal or not. I know, it doesn't seem to matter with no runners on, but it is the way FED wants the pitching regulations called. 
 
As far as this "throwing off the pitcher", 2 options. 
1. Move the free foot back to where the heel is touching the rubber when he starts his windup. He can move the foot foward when he starts his windup, so I don't see how it throws one off. If it does, then option 2 is just pitch from the set all game. 

Sorry. You kicked this one. The batter has to hit the ball to be called out. FED 7-3-2
 
Hit the ball fair or foul while either foot or knee is touching the ground ­completely outside the lines of the batter's box or touching home plate.

Legal in OBR. Obstruction in FED.

Appealing a base left too soon is a time play. The run scores if he crosses the plate before R2 is tagged or 2nd base is touched. The fact that only the base need be touched on an appeal to get the out does not make this a force play. 

And the answer to the title of this thread is...Never.