3) I really don't understand why every one has such trouble with this play. I guess it's because the announcers were confused. Announcers don't understand clock management and clock rules. Ignore them.
Once the TD was called back, Belichick called the time out. He did so because if he had not, the clock would have started to run as soon as the umpire placed the ball on the field for ready to play.
Once the TD was called back, they treat it like a completed catch. Since it was in bounds, the clock would begin once the reply overrule happens.
Belichick called the time out to keep the clock from starting. He was hoping that the Bills would be stupid and try to score on the next play, preserving 1:40 for the Patriots. If he hadn't called time out, the refs would have placed the ball, winded the clock, and it would have ticked down to 1:10 or so.
The reason Belichick was going crazy was that the clock operator had run off a lot of time after the TD call, which was true but ultimately irrelevant.