Possibly. Referee can do lots of things during a game that may not be right but that does not mean they cannot do it. My guess and it is only a hypothetical question, is that they could if they so desired.
The referee has the right to smack that player in the face
The bench on a basketball court is positioned along the side, parallel to the length of the court. Each team's bench is separated by the tables for the shot clock operator, scorers, replay officials, and commentators.
if the coach does a penalty against the referee or the other team. if the coach mouth talks to much to a referee he could get a bench penalty
Bench
He can if the stick is broken or the player has another stick or he goes to the bench
17 including coaches
Segregation
It depends on where they are...
The head coach is the leader of the bench. If a technical gets called on the bench in general as opposed to a specific player or coach on the bench, the technical goes to the head coach.
the referee There are a number of officials on the field for a game. At the highest level, there are a referee and two umpires on the field. Off the field, there is a bench official (timing and score) and a box official (penalty box and substitution area). At the lowest level, all these functions are performed by a single official, the referee.
Coach Carter
No, but they do make the recommendation(s) to league commissioners, and/or the governing bodies who then make the ultimate decision(s).