As per 5.8.3 I'll just do the last part of my question. It states, Team A may, but Team B may not be granted a time-out after the ball is at A's disposal. I thought on a throw-in there is no team-control. So why could Team B not be allowed to call time-out if the clock is stopped and there is no team control.

chrs_schuster,

5-8-3a. "at the disposal"

NCAA fixed their similar rule by stating that team control exists "at disposal" (or similar wording).