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A sacrifice fly is a fly ball that is caught for an Out, but that allows a runner to tag up and score. A sacrifice bunt is a ball that is "tapped" with the intent of sacrificing an Out (the batter) to advance the runner or runners on base.
Yes, provided he has control of the ball at the time.
If the batter/runner is contacted by a fair ball when they are out of the box they are out and the ball is dead thus no runners can advance. Given this the answer to you question is no they can not score.
If a runner is touched by a fair ball in fair territory before the ball has touched or passed an infielder, the runner is out. The ball is dead and no runner may score. And no runner can advance, except runners forced to advance. [Rule 7.08(f)]
when someone hits the ball and it is caught, the runner(s) on base can "tag" the base they are on once it is caught and then run to the next base. If they tag 3rd base and run home to score it is the tag run.
No, it is not considered a sacrifice unless the batter is advanced as a result of a bunt. Also, a fly ball that is caught is only considered a sacrifice if a runner tags and scores on the play. If a runner tags at 1B or 2B on the caught fly ball, and advances one base, it is not considered a sacrifice fly.
No. With minor exceptions (e.g. a fielder with the ball can tag "out" a runner) baseball is NOT a contact sport. A catcher holding the ball and blocking off home plate CAN legally be barreled over by a runner attempting to score by knocking the ball out of the catchers hands but other than that, no there is no tackling in baseball.
because without one all the runners on base would be able to score on a high pop up on the infield the tag up rule is a compromise between that situation and not allowing the runners to advance at all after a ball is caught
According to MLB rule 7.08(f) "A runner is out when ... He is touched by a fair ball in fair territory before the ball has touched or passed an infielder. The ball is dead and no runner may score, nor runners advance, except runners forced to advance." Since the ball is dead the instant it touches the runner, where it goes afterwards is irrelevant.
If a batted ball is caught in the air, the batter is out and would not be on base. It would not be a "hit."