Is the hand, when in contact with the bat, considered part of the bat, and thus if hit a foul ball is called? If so, where might I find it in the NFHS rulebook. Thank you.

No it is not in any rulebook. Whenever a batter is struck by a ball it's dead. What you do with it depends on what happened. If he is swinging and he is hit, hand or anywhere else, it's a dead ball and a strike.