Yes. Any part of the bat is fair game. Sometimes, a pitcher will throw the ball up and behind the batter's head, and if the ball strikes the bat it counts as a foul ball - and if it pops into the air, and the catcher catches it, it is an out!
It is a Home Run.
If the baseball hit the ground in foul territory, the ball is a foul ball. If the baseball hit the ground in fair territory, and the batter/runner is still in the batter's box when the baseball hits him, it is a foul ball. If the baseball hit the ground in fair territory and the batter/runner is out of the batter's box when the baseball hits him, the batter/runner is out and the ball is dead.
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.
its a dead ball and a strike, but not strike 3, just like a foul.
A ground ball its fair. A fly ball is foul.
it is a foul.
If the batter is outside the batter's box, and is in fair territory when the ball hits them, then yes they are out. If they are in the box, or in foul territory when the ball hits them, it is just a foul ball.
fair ball
In regular baseball rules, the ball is still live, even if it hits the ground first, until it hits the batter, then it becomes a "dead ball". If it never hits the batter, its still a live ball.
If a pitched ball hits the batter, it is dead, and all runners must return to their bases.
Batter hit the ball into the outfield.
Fair ball.