Batting out of order, DH rule, and pitch count

[CoachJW]

This is a high school JV game in California between friendly rivals that ended 8-0 in favor of the visitors. I was the scorekeeper (and parent of a player) for the visitors and the home team did not provide a scorekeeper. None of what follows would've changed the outcome. However, I'm interested in these things and I want to know how the umpire and/or coaches should have handled it.

The home team batting order to start the game has this at the bottom:

8. #21, playing 2B
9. #11, DH

#16 is playing RF and they're DHing for him, he's not in the batting order.

They take the field in the top of the 1st and #11 (the listed DH) is playing second base.

In the bottom of the second inning, the home team gets to the 8th hitter in the batting order and #11 comes to bat (out of order) and strikes out. #21 follows him and also strikes out.

In the third inning, the RF #16 is subbed out on defense for #6. #6 plays RF the rest of the game but does not bat.

Later in the game #11 and #21 come to bat in the same order and strike out again. #11 played second base the whole game.

What could the visiting coach have done to appeal any of this?

Unrelated--the pitch count. The governing body has a cap of 90 pitches in a game for a pitcher at this level. The home team pitcher reached his 90th pitch during a plate appearance, then continued on for a few more hitters and got to 100 pitches. The umpire said he has nothing to do with the enforcement of the pitch count rules. Does that vary anywhere else?

Thank you for your feedback.