SP (ASA) Ball hitting batter.....

In the first situation, where the batter was hit by the pitch, I would declare dead ball right away and runner returned to 1st. No penalty for not getting out of the way. If you look at the ASA rule book, it clearly states that the ball is dead if it hits the batter and no play can happen.

Second situation, where the batter caught it, would have been a dead ball, no penalty because there's nothing in the rules that states the batter can't do that (I've looked myself and can't find anything that would reference that). However, I would warn the batter about doing that because it puts both teams at a disadvantage.

Last situation is just a dead ball. No penalty.