Scoring Runs

Can you score a run after the 3rd out?

Play 1:
Bases loaded, two outs, batter takes ball four. R3 walks slowly to the plate as R2 aggressively advances to 3b, rounds the base and is tagged out. The out on R2 happens before R3 touches the plate.  Ruling: Score the run on the live-ball award
Play 2:
With two outs and base runners on second and third bases, the batter singles to right field. The lead runner misses home plate but the trailing runner (who started on second base) is thrown out at the plate for the third out. Immediately after the play, the defense appeals the lead runner missing home plate.  Ruling: The defense is granted an advantageous fourth out which supersedes the tag at the plate and negates the apparent run.
Play 3:
An out is made on the bases in addition to an out on a properly appealed checked swing. Ruling: the checked swing out is assessed before the out on the bases.
Play 4:
R3 scores on wild pitch, passed ball or dropped third strike and the batter does not run. R3 is safe then the throw to 1b on BR is made for the 3rd out. Ruling: no run scores.