DH question

I believe you are correct, although my head is spinning.  The new pitcher has replaced the shortstop.  The DH is lost when:  a.  The player being DHed for enters the game (in the DH's spot) as a batter or runner, or:  b.  The DH assumes a defensive position.  Neither has happened, so the role of DH is not terminated.

Yes, all the other moves are irrelevant. Just mentioned them to show that everyone else stayed in the game. But essentially, all that happened in relation to DH is that the new pitcher replaced the SS. 

In HS, the DH shares a batting order spot with a defensive player (he doesnt bat for a specific person or for a specific position).  If the defensive person in that spot is replaced, the DH is batting for the substitute.

The moves you describe are legal.

The answer is, it depends -- in this case, on what the coach wants and how he therefore reports the substitution to the HPU.

The new P has to enter the lineup into the batting order slot shared by the DH and the former SS.  He can do this either by the team keeping the DH and having the new P be only a defensive player, or he can do this by taking over for both the SS and the DH and therefore both pitching and batting.  If you do the latter, the DH is destroyed for the game.

Typically you would retain the DH in that situation.  For one thing, if the new P were deemed a better hitter than the DH, wouldn't he have been the DH in the first place?  For another, the head coach should consider the possibility that the new P has a bad outing and has to be yanked before his team even gets up to bat again. 

So I would expect the DH to be retained, but under the rules, the head coach does have a choice to make.

I could be wrong (and it will definitely not be the first time) but under NFHS rules all starters have one re-entry including the DH.  So if the new pitcher came into that spot and both the SS and DH were no longer in the lineup each one would have one opportunity to re-enter.  But if they do re-enter then that new pitcher is done since he was a sub. 

You are correct that both starters (F6 and the DH) can reenter.  But, if the new P replaced both, then the DH as a "role" is done for the day.  The team has gone from a 10-man lineup to a 9-man lineup and can't return to a 10-man lineup.  The PLAYER who was the original DH can enter, but he'll have to play defense (or be subbed for when the team goes on defence).