Force Out(s)?
 

Tie game, bottom of seventh inning, bases loaded, one out, ISF rules.

Batter takes ball four, runs and tags 1B. Runner on third advances tagging HP. Runners on first and second advance half way to the next base, turn and head for the dugout. End of game?

Pitcher picks up ball throws to 3B, who tags base and throws to 2B. Second baseman tags base.

Is the game over, or are we in the eighth inning? Any difference if the first base tagged was 2B and afterwards thrown to 3B?

Game over in my book

Game over also in my book.

I don't know about ISF, but in ASA, when a walk is awarded, all runners, including the batter-runner, must complete their baserunning responsibilities and touch all bases awarded.

So in the OP, assuming R1 on 3B, R2 on 2B, and R3 on 1B... if R2 and R3 haven't left the field of play and entered the team area, I got nothing on the appeals. They can get to their awarded bases however they choose.

If they have entered the dugout, then I have two forceouts to end the inning - not because of the appeals, but because they left the field of play. No run can score when the 3rd out is a forceout, so I still have a tie game and we start the 8th inning.

(ASA Case Play 8-6.1)

SRW, I am with you 95% of the way. Your cited case play has 2 outs, so the difference isn't part of the case play. The 5% difference is the order in which the baserunners leave the field of play.

If R3 from 1st enters the dugout first, then R2 from second is no longer a forceout when she enters the dugout. The third out would then be a timing play; did R1 touch home before R2 left the field?

Good point, I didn't think of that. Order of who entered the dugout would apply in the OP... makes it either a force out or a timing play. Good catch! :)

How many of you would call the outs in this situation if the defense did not indicate (by, for example, not leaving the field of play or making an "appeal") that they knew the offense made this mistake?

If this happened to be a one-umpire game, I find it hard to believe it would be caught whether the defense knew about it or not.