Missed Base on Tag Up

 
With one out and the bases loaded, the batter flies out to the right fielder for the second out of the inning. The runner on third base (R3) properly tags up and easily scores because of a poor throw to home plate from the right fielder.
 
However, the runner on second base (R2) went halfway to third base on the fly ball to right field. When he saw the poor throw to home, he advanced to third base and then home plate and scored (but without properly tagging up at 2nd base).
 
The defense then properly appeals that R2 did not properly tag up. The umpires agree and call R2 out for the third out of the inning. Of course, R2's run does not count... but does R3's run count?
 
Bonus Question: In the play above, what if R3 did NOT properly tag up, but R2 did properly tag up. As in above, both runners crossed home. The defense properly appealed R3 failure to tag up and the umpires call R3 out for the 3rd out of the inning. Does R2's run count?
 
Call
An appeal of a runner failing to properly tag-up is a timing play. If runs score before the umpires rule on the appeal, then those runs count. When a lead runner is called out on an appeal, and that appeal is the third out, no runners following that runner can score. In the situation below, R2 was called on appeal for the 3rd out of the inning -- but after R3 had scored. In this case, R3's run counts.

For the bonus question, R3 was called out for not properly tagging up at third base. Since this was the third out of the inning, any runner following R3 can not score.