MadMax

Yes in both codes, provided the “new” player meets the eligibility requirements for the league or conference. 

If pitcher (F1) definitely stepped off, as you stated, then it’s 2 bases. Thus, R2’s awarded Home.

It’s a foul ball. The batter setting up for a bunt attempt is not yet a bunt. His pulling the bat back is no longer a bunt attempt. The pitch hitting the bat, in such a manner, is akin to the pitch hitting the knob on a pitch up-and-in, or hitting the bat while the batter is dropping it while ducking a pitch behind him. Are those regarded as swing attempts? No. However, once the pitch hits the bat (first), the ball becomes subject to a fair/foul judgement like any other batted ball. 

As long as the Retired Batter-Runner (BR) doesn't intentionally make contact with the thrown ball, then this is nothing.
Tell F9 (Right Fielder) to make a better throw.

In NFHS (Fed) Ruleset: 1 foot in, 1 foot out is fine.
In Official Baseball Rules (OBR): Both feet in, but on the chalk is considered in.
Here’s the thing, though. In either Ruleset, there is simply a “There Shall Be” statement, stipulating that 7 fielders shall be within Fair territory (as detailed above), while the Catcher is to be in Foul territory, and the Pitcher shall be legally engaged to the pitcher’s plate (rubber) so as to make a pitch legal. There isn’t a penalty delineated. Besides this, if a First Baseman (F3) wants to stand in foul territory to receive pickoff throws, he can ad infinitum. Why? These aren’t pitches. So, if that same F3 shuffles into Fair to defend his position while the pitcher delivers a pitch to the batter, what’s the problem with that?
A “fielder’s balk” is a myth.
Do as @Rich Ives mentions. Umpire should just remind or direct that F3 (or any other fielder) should be in Fair territory, and leave it at that.

Hm.
Hmmmmmm.
How much baseball have you watched? How much baseball have you played? ... Better yet, was this game being played in some remote, exotic locale that was introduced to baseball via a partially intact rulebook that washed up on shore?
The pitched ball you stated was fouled into the stands is dead. D-E-A-D. No subsequent activity can be valid until a replacement ball has been made live.
A replacement ball can only be made live by the ball being in the pitcher's possession – having gotten there from catcher, umpire, coach, aerial parachute team, a trained Golden Retiever or otherwise – and the pitcher re-engaging the rubber, batter back in the box ready to bat, and the umpire signaling "Play", thus making the ball live.
Nothing would be scored any differently, because no scoring occurred.

R2 (lead runner, as you called it) committed the base running infraction. Since that is the 3rd out, neither his run nor the following run scores, and the inning – and game – is over.

Yes. So long as the ball is in secure possession by a/the fielder, any part of the body contacting the base prior to the arrival of the Runner constitutes the ball beating the Runner there, thus is an out. The fielder can sit on the bag for all we care.

Then you, sir, are in the wrong forum. 
 
... But I'd probably register that as a strike. Wicked googley.