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1. It is not a violation to leave the floor during a dead ball.
2. It is not a technical foul to leave the floor when the action does not involve showing disgust or resentment.
3. The team member coming from the bench did enter illegally because he was not beckoned in by an official (perhaps he checked-in at the table, perhaps not).
4. With technical fouls, substitutes are permitted prior to the first free throw.
The correct administration for this situation is a personal foul by A1, then an unsporting technical foul by A1 (for running his mouth), and finally a technical foul charged to the illegally-entering substitute per rule 10-2. No indirect technicals are charged to the head coach.
Don't know if Team B is entitled to FTs for the initial foul by A1 (the personal foul), but four FTs are warranted for the two technical fouls.
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