Team training is usually good for 2 game weeks. You can still do normal training. Just be prepared to change to a new trainee once you get your new players from the draft. Team training is a bit different. If you are going to be training FTs/stamina, then your best bet is to not waste money on a trainer at all. A lvl 4 trainer trains the same as lvl 1 trainer for these type of training.
I wouldn't recommend you buying players at this stage. They are all going to be more expensive than usual as teams buy players for playoff runs and they will all go up in age in a few weeks time. You are better off waiting till after the draft. Buying/selling players will NOT affect enthusiasm. It will annoy the fans via the fan survey as they prefer to see constant faces in the team.
Trainer has no effect on enthusiasm whatsoever. You gain enthusiasm by telling the team to take it easy in games and you lose enthusiasm by telling them to crunch time. Gradually enthusiasm will move towards 5 if you constantly play normal.