1) First day of the season
2) Counters will count. You can appeal for a medical hardship waiver but I'm not sure if that is done before the season or at the end of the semester. If I'm correct, they go thru the season normally and sort out the appeals afterwards when the season is over and playing time is already determined (although not positive). Depending on when the surgery was and if a Dr. releases him will factor into that decision. But if a Dr clears him to play for April the appeal most likely won't go his way.
3). This is a good question (one I've asked on here before) and I'm not sure. In FoxDad's case I'm not sure if it was academic money or athletic money that was cut, but if the draft doesn't go in favor of a team or players are granted another year- there are players that find out as late as August that they won't have their scholarships renewed. I would assume that it has to be done before move in day. I don't believe you can have more than 11.7 "scholarships" walking around campus at any time. Regardless of cuts or transfers.