When does designated bench personnel become the HC following DQ of the HC?

[La Rikardo]

Adult bench personnel for Team A are as follows: A Head Coach, A Assistant Coach 1, and A Assistant Coach 2.

Prior to the game and after the officials' jurisdiction has begun, team member A1 dunks a dead ball. A1 is charged with an unsporting bench technical foul; this foul is also charged indirectly to A Head Coach.

During the first quarter, A Assistant Coach 2 addresses an official disrespectfully and is charged with an unsporting bench technical foul; this foul is also charged indirectly to A Head Coach.

During the second quarter, a fight breaks out on the court. Bench personnel team member A6 leaves the confines of the bench during the fight. A6 is charged with a flagrant bench technical foul and is disqualified; this foul is also charged indirectly to A Head Coach. A Head Coach is disqualified for having been charged with three technical fouls. A Assistant Coach 1 is designated as A Head Coach's replacement as head coach for Team A.

(a) Before or (b) after A Head Coach is informed that he has been disqualified, A Head Coach disrespectfully addresses an official and is charged with an unsporting bench technical foul.

Shall A Head Coach's foul be charged indirectly to A Assistant Coach 1? If not, when does A Assistant Coach 1 officially become the head coach for the purpose of being charged indirectly for bench technical fouls? Additionally, if A Assistant Coach 1 is not charged indirectly with a bench technical foul, may he stand within the coaching box?