What if pitcher hits batter?

Answer 1

The runner is safe, in order for the runner to be considered out the fielder would have to have the ball in his glove or hand and tag the runner.

*edit: It depends on where the runner is when he is hit. If the runner is running a direct path to first and is within the 3ft baseline, the runner is safe. If however the runner takes a lane outside the 3ft path, in a deliberate attempt to block the catcher's throwing lane, the runner is out for Interference.

Answer 2

If the pitcher hits the batter on a pitch then the batter is awarded first base. However if the batter swings at the ball and it hits her then it is a strike