Does a runner get a run/score if the 3rd out is made (caught or thrown-not strike)before he crosses home plate?

If the batter makes the third out, either by hitting a ball that is caught in the air by a fielder, or hitting a ground ball and being thrown out at first, the runner can't score from second...even if he crossed home before the third out was made.

As dawgdays noted, same goes for a force play. So if there's a runner at first and the batter hits a groundball to short, and he steps on 2nd before the runner from 1st reaches 2nd, the runner is out on a force and no run scores.

Timing does matter when it isn't a force play. Say runner on 1st with two out, batter hits a line drive to right-center. The batter rounds 1st and is half way to second when the throw from the outfield is cutoff by the 1st baseman, and the batter gets into a rundown between 1st and 2nd. If he is tagged out before the runner from 1st can come around and score, the run doesn't count. However, if he avoids the tag until after the runner has scored, then the run does count.

If the third out is made before the runner reaches the plate, the run does not score.

The run also does not score if the third out is made on a force play, or on the batter-runner before he reaches first base, even if the runner reaches the plate before the third out.

[Note, an appeal out for failure to tag up is not a force play, even though the out can be made by tagging the base.]

No. The runner does not get a run/score.

No. Runner must touch homeplate before the 3rd out is made.