Removing the helmet
 

What is the penalty for a player removing his own helmet for a non equipment issue during a dead ball period. Or is there no such rule in NFHS?

There is no such rule.

The only way a penalty could be assessed is if the player did so to bring attention to himself. But simply removing a helmet is not illegal in itself. College rules are a little more explicit in removing the helmet and in your example that is not a foul either.

Peace

What Rut said