1) To me, "carrying" is pretty obvious. If you don't "carry the ball" during a high dribble, then it's not a violation
2) I don't know how many times I've told (mostly rec league) coaches to stop complaining about the other team "reaching". Reaching isn't a foul.
3) There can (and probably will be contact). I look for displacement that is either severe, or creates an advantage.
4) Because no team has team control when the ball gets stuck. The way I think about it that makes sense is: Both teams would be entitled to a rebound if the ball doesn't get stuck. Team A didn't put the ball out of play (the basket is in play). They simply missed a shot. Therefore, they would get equal chance at rebound. So ... Jump ball is fair.
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