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(1 & 2) Correct. When time has expired at the end of the game shoot all pending FTs up to the point where it is mathematically impossible for the outcome to change based on the remaining FTs due.
In your last case, you must have a typo. The team that you had as being ahead then made a bucket to tie the score. I'll assume you meant team A was behind and made a shot to tie. You are correct in your conclusion. Since the quarter ended with a tie, the quarter is over. Overtime will be played and coach A's action are penalized at the start of OT.
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