You might want to get a little more experience on how a team runs then re-answer your questions. The head coach deals with the Athletic Department, Boosters, office staff, assistant coaches, recruiting coordinators... etc. They have very little time to actually be around the players.
That is what the assistant coaches are for.
"who is responsible for discipline on the team?"
Assistant Coaches
"Who is responsible for [enforcing] team culture?"
Assistant Coaches
Everything is the head coaches fault... Fact. However, he has very little to do with everything.