[CoachPaul]

Problem 1
1) no, irrelevant
2) no

Problem 2
An MLB team would never bring just nine, so I'll make the assumption that this is a youth game. If this is a youth game, many leagues allow for starting with 9 or more and finishing with fewer than 9. In those cases, the batter is out when his time comes. The team does not automatically forfeit at the youth level.
If we are assuming the entire MLB roster ate at Chipotle's before heading over to the stadium and only those lucky 8 remain to play...
1) OBR does not allow for playing with fewer than 9-- that I can find.
2) I'm thinking the game should have been forfeited at the moment of the ejection. The roster submitted before the game would have only had 9 names on it. No way to continue. IF the team were smart they would have signed a bullpen catcher or two to one day contracts for $1 and added them to the roster for such a contingency.

Problem 3
1) Unless the umpires get together and reverse the call, the game is over.

2) It would have had to be obvious to one of the umpires to initiate the reversal.

3) It was weird. I would have plated R3 and advanced R2 to third and put the BR on first with two out.

4) No, once you have confusion, you just try to set it as right as possible--assuming the original 3rd out call is reversed.

Problem 4
Had the runners retouched, their runs would have counted because it was a timing play due to the 3rd out not being recorded by a force or before the BR reached 1st base.
Had the defense not appealed, the visitors would have won. With the appeal, the home team preserves the victory by recording the virtual 4th out on R3. On a play like that, the home team would ALWAYS appeal--even if they didn't know for sure if R3 retouched (just in case).

Problem 5

R2 legally scores. R1 has rights to 3rd base and is safe when tagged and the BR (aka B9/B5) would be out when tagged since he has no claim to 3rd base. Two outs and we play on.