Bat check, was any of the handle showing through the loose tape? I always make them fix loose grip wrapping.
Obstruction, as you stated no such thing as umpire obstruction. Shame on umpire for being in the way, but the out stands.
Illegal pitch, coach can argue all he wants, the rule book says the pitcher must take position with the hands separated, and while separated simulate taking a signal. If you judge the hands coming together is immediate, then it is an illegal pitch.
Runners leaving bases during time out, you are applying NCAA rule to high school ball. Nothing restricts the runners to their bases during a time out. As long as they are ready to play at end of time it is fine.
Obstruction at 1st, if you had her obstructed prior to 1st base, good call. If she was obstructed while rounding 1st, she is protected between 1st and 2nd. If tagged out she should have been awarded the base she would have reached absent the obstruction.
HBP strike, if it caught the zone it is a strike. If it hit her after that it is a dead ball strike.
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