No, once you are tagged out you don't get credited with anything if you are the one at bat. Now if another batter hits the ball and there was already a man on base at first and he gets tagged at 2nd base, then yes the man on 1st base would get the single from his previous at bat If the batted ball was cleanly a base hit and he was thrown out trying to advance past first base then the batter would be given the hit corresponding to the last base the batter reached safely. If the batter was thrown out at second, the batter would be given a single. If the batter was thrown out at third, the batter would be given a double. If the batter was thrown out at home plate, the batter would be given a triple.
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That would depend on how the runner was retired at second base. For example, if the runner slipped and fell on his way to second base and the outfielder had the time to throw him out on a force play, the batter would not get credited with a base hit. If the runner made it to second base safely and then slipped rounding the bag and the outfielder threw to second base and the runner was tagged out, the batter would be credited with a base hit. If a runner is forced out at any base, regardless of where the ball was hit, the batter is not credited with a base hit.
Yes, the batter made it safely to second base. Therefore, he is credited with a double.
Yes. it is a single. If the runner makes it to second on an error it is also a single.