Once the HEAD coach has been disqualified does someone who is bench personnel get charged with indirect technicals if the situation arises or do we just ignore them? e.g. team members leaving the bench during an altercation or a team member receiving a direct T while on the bench or after being disqualified, but while still on the court.

What if the HEAD coach was DQ'd for a direct and two indirects, do the two indirects have any carry over to the new designee, if one is allowed?

I don't believe that the NFHS rules address either of these situations.

When the Head Coach is disqualified, one of the assistants on the bench must be the new "head coach" for the rest of the game. In PA, that new hc will have lost all standing privileges for the remainder of the game. However, the new hc does not inherit any technical fouls for becoming the new hc. If the assistant had a direct T before becoming the new hc, then he/she would still have that direct T. But if the assistant was clean, then he/she would still have full allotment of direct/indirect Ts before becoming disqualified.

While I agree with the fresh start, but no box (BTW does PA even use the box? I didn't think so.) I wish to know if you are stating the above as a fact for all NFHS play or if that is only the way PA does it.
In other words, do you know for sure how the NFHS handles it? I can't find a specific rule that states this.
It makes a difference for time-outs.