Lead Runner Misses Home

 
With 2 outs and runners on second base (R2) and third base (R3), the batter (B1) hits a double down the right field line. As R3 is about to touch home plate, he sees B1's bat on the ground, so he picks it up -- but in doing so, he fails to touch home plate. R2 scores easily after that. R3 worries that he may have missed the plate, so he then walks over and touches the plate.
 
The catcher noticed everything: the miss by R3, then the touch by R2, and then the touch by R3. After the play ends, the catcher then appeals to the plate umpire that there was a missed base by R3 and there should be some penalty.
 
What does the umpire do now?
 
Bonus questions:
1. Does the answer change if there is one out when this play started?
2. If the defense does not notice the missed base, what is the action by the umpire?
 
Call
A run is not scored if a runner advances to home on a play in which the runner ahead of him is declared the third out on appeal for failing to properly touch a base (NF 9-1-1c).
 
So with two outs, upon proper appeal, R3 is declared out (for the third out of the inning) and runners after him (R2) do not score. If there were only one out, R3 would still be out (for the second out of the inning) but R2's run would count. In each situation, it is up to the defense to initiate the proper appeal.