DH - Re-entering question

[cbfoulds]

Originally Posted by cshs81

A pinch-runner comes in for the DH.

I'm assuming the following:

1. There is no more DH for this game for this team.
2. The player that was the DH can re-enter the game.
3. If so, if he comes in for the player that was being DHd for, that's simple.
4. If he comes in and the coach removes a player that is batting, the player that was being DHd for now slides into the removed player's batting slot.

Correct?

1) False [assuming the runner is NOT the DH's defensive counterpart]
2) True, as the DH or on offense
3) True
4) False: both the DH and the offensive player counterpart are, like everyone else in the batting order, locked in place in the batting order. Nobody in the batting order can "slide" into a different slot.