Yes the ball is dead, and no the runners cannot advance.
Ball's dead and runners can't advance.
batter is out, runners do not advance
No the ball is dead as soon as it hits the batter, no runners may advance more than one base.
If a better puts out his bat for a bunt and does not pull it back, the pitch counts as a strike (as long as the ball does not hit the bat of course). It does not matter if the ball is in the strike zone or is 10 ft outside of it. Given that it is a strike, the runners do not advance, although they can attempt to steal.
All base runners advance 3 bases and the batter is not out.
If, in the judgment of the umpire, the action by the batter was intentional, the batter will be called out. If, in the judgment of the umpire, the action by the batter was unintentional, the ball is alive and in play. Rule 6.05(h) states: "After hitting or bunting a fair ball, his bat hits the ball a second time in fair territory. The ball is dead and no runners may advance. If the batter-runner drops his bat and the ball rolls against the bat in fair territory and, in the umpire's judgment, there was no intention to interfere with the course of the ball, the ball is alive and in play"
If a batted ball hits a base runner in fair territory before the ball has been touched by a defensive player or an umpire, the ball is dead, the runner is called out for interference, the batter is awarded first base, and all other runners advance one base if forced. If, however, the ball has been touched by a defensive player or an umpire before hitting the base runner, the ball is live and play proceeds as usual (unless the runner is judged by the umpire to have deliberately made contact with the ball, then the runner can be called out for interference, the ball is dead, the batter is awarded first base, and all other runners advance one base if forced, or, if flagrant, the batter can also be called out and no runners advance).
If a batter gets a base hit to the outfield that would normally be a single but the ball goes through the legs of an outfielder and the batter winds up on third base, the play would be scored as a single and an error on the outfielder. Depends on the determination of the "official scorer". If the ball goes under the outfielder's legs and, in the official scorer's opinion, it could have been fielded with ordinary effort, and the batter or runners advance an additional base or bases, it would be an error allowing the runners, and/or hitter to advance. If, however, the ball goes under the outfielder's legs and, in the scorers opinion, could not have been fielded by ordinary effort, an error is not necessarily scored on the play.
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 batter hits the pitch, either fair or foul, with all of one or both feet completely out of the batter's box, he's out. The ball is dead, and no runners can advance.
No. A sacrifice is when the batter turns around to bunt and lets everyone on the defense know what they are going to do. The batter is 'sacrificing' (allowing the defense to get him/her out) so the runners can advance one base.
If a runner is touched by a fair batted ball, in fair territory, before passing a fielder, it's interference, the ball is dead, the runner is Out, and all other runners must return to the base occupied at the time of the pitch, unless forced to advance due to the batter being awarded 1B on the play.