1. In some of the sports if a player at the college level reaches a certain age by a certain date an is performing well enough he's draft eligible and can be listed regardless of his wishes on it.
Basketball has a minimum age of 19. It wasn't always like that. They used to draft kids right out of high school. Some of the kids today under 19 go to Europe to play until reaching 19.
I believe the player has to put his name in the draft. That is, he has to say he's eligible for the draft. At least for basketball and football. I'm not sure about baseball.
2. Once drafted he can accept or refuse a contract, if he refuses he can't play for any pro club for a set period, if he accepts he can work a deal on the pay (within limits) and a start date - thus he can leave school or finish school if they negotiate it right.
If drafted, he can't play for another team in the same league. But he can in another. That was my example of someone good enough to play in both baseball and football. John Elway was like that.
You must be right about start date because the San Antonio Spurs basketball player David Robinson was drafted but finished his military service before joining the team. But each sport is different.
3. The contracts include basic salary plus a performance bonus schedule and a bonus schedule for other events like PR activities and training activities.
And maybe a signing bonus. And I don't know if every contract has a performance bonus.