Runners Missing Bases... Again

 
With the bases loaded and two outs, the batter (B1) hits an inside-the-park home run, but R1 (who started the play at first base) missed 3rd base. At the end of playing action, the defense calls "time" and properly appeals that R1 missed 3rd base. The umpire calls R1 out for the third out. The inning is over, but four offensive players crossed home plate. How many of those runs score on this play

Extra Credit: On the play above, what if B1 is tagged out at home plate for the third out of the inning. It looks like 3 runs scored on that play, but can the defense still appeal that R1 missed third base (for the 4th out of the inning)? If they can appeal, how long do they have to make that 4th out appeal?

Super Extra Credit: On the original play above (where 4 runs safely crossed the plate), what if that 4th run scored (B1's inside the park home run) ends the game with a home-team walk-off one-run win. Can the defense still appeal that R1 missed 3rd base (and take runs off the board and get a win or a tie for the visitors)? If they can appeal, how long do they have to make the 3rd out appeal?
 
Call
Since the defense properly appealed, R1 is out. The runners that scored before R1 will have their runs count (R2 and R3), but the runner that scored after R1 (B1, in this case) does not count.
 
It is rare, but a defensive appeal can generate a 4th (or even a 5th) out. Inning-ending appeals can be made as long as there is at least one infielder still in fair territory. If the defense makes a proper appeal, R1 is the 4th out. The two runs that scored before R1 (R2 and R3) count -- but R1's run does not count. 
 
A game-ending appeal has yet another set of rules. If the appeal is made before all the umpires have left the field of play (entered dead-ball territory), then the appeal can be considered. In this case, if the missed base is properly appealed, then R1's and B1's runs do not count. The home team does not have a walk-off win -- instead, they lose the game by one run. (Lesson learned for umpires  -- minimize the time between the end of the game and your exit from the field!)