Yes the ball is dead, and no the runners cannot advance.
it is a foul.
If a pitched ball hits the batter, it is dead, and all runners must return to their bases.
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, the ball is not dead and the batter may attempt to hit it.
It is ruled a dead ball and each base runner would advance one base.
An umpire is not supposed to throw the ball back to the pitcher with runners on base. If he does the ball is dead from the time he touches it to the time the pitcher has the ball on the pitching mound. So the runners cannot advance.
No. You answered your own question. The ball is dead if it comes into contact with the batter. Play should immediatly halt. I can see in softball, if the fourth ball is pitched and it hits the player, and is counted as a ball, then both runners would move. Of course if the runners on base are forced runs. Aside from that. I cant see a scenario where the runner would move bases based on a dead ball.
Yes. Ball is dead. Batter is awarded 1st and all runners advance 1 base. Rule 5.09 (f)
Yeah they can. They can only stay put if the ball is caught as a fly.
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.
There is no such phrase in baseball as "full play." The closest I can think of would be a "Triple Play" where two runners are on and the batter hits the ball and both runners and the batter are put out on the same play.