If a base runner is hit by a batted ball before the ball contacts, or passed an infielder they are out... once the ball passes, or is contacted by an opposing player there is no penalty for being hit.
With a note at the bottom.
It is credited as a put out for the pitcher.
If a runner in fair territory is struck by a batted ball prior to the ball having been fielded, the runner is out.
If a runner is touched by a batted ball while off base before the ball passes an infielder (other than the pitcher), it's dead ball, runner is out. If the runner is on base when touched by a batted ball, it's live ball and play continues.
No...as soon as the batted ball touches the runner, the ball is dead.
No. If a batted ball is touched by a defensive player before it touches a runner, the ball is live and the runner is not out. Also, if a batted ball passes a fielder that could make a play on the ball and touches a runner, the ball is live and the runner is not out. This situation is very rare and would only occur when the infield is playing in and are in front of the runner(s).
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.
No
From the official rule book Rule 7.08: the runner is out if "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. EXCEPTION: If a runner is touching his base when touched by an Infield Fly, he is not out, although the batter is out; Rule 7.08(f) Comment: If two runners are touched by the same fair ball, only the first one is out because the ball is instantly dead. If runner is touched by an Infield Fly when he is not touching his base, both runner and batter are out." Rule 7.09 is also relevant. The runner is not out if 1) the ball was first deflected by a fielder or 2) if the umpire is convinced that the ball went through or past the fielder untouched, and in the umpire's judgment no other infielder had the chance to make a play on the ball.If, in the judgment of the umpire, the runner deliberately and intentionally kicks such a batted ball on which the infielder has missed a play, then the runner shall be called out for interference." However, if in the umpire's judgment the runner intentionally kicks the batted ball, the runner shall be called out for interference. If a runner is touched by a batted ball in foul territory he is not out though.
No it is a dead ball
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)]
Yes.