If a player is going to school on basketball scholarship and declares the NBA draft and does not get a contract can he still use the scholarship to finish school?
Basketball is one of two sports where you may initially declare/be eligible for the draft but return to college (The other being baseball, which does not require players to declare and therefore players have not taken any action to reduce their eligibility even if drafted - hence, players are frequently drafted two or three times during their amateur career).
The NCAA explicitly exempts basketball in this note:
Basketball student-athletes may enter a professional league’s draft once during their college career without jeopardizing their eligibility as long as they are not drafted by a professional team and as long as they declare their intention to resume playing for their college team before the first day of the spring signing period, typically in April.
The significance of the timing here is that players must withdraw from draft eligibility prior to the draft, which takes place in June. A player who remains on the draft eligible list but is not drafted may not return to NCAA competition; often these players will leave and go overseas.
This is a relatively new rule (2011); prior (2009) it was in mid-may. It is largely to allow coaches to better plan scholarships, since the spring signing period is when they go recruiting.
You also may not have retained an agent, although this may change in the future; one of the major problems with the NBA draft is players feeling they are ready and then not being drafted because they get bad advice. Agents would have an incentive to encourage entering the draft, so allowing agent contact would be fairly complex.
Yes. You can declare but are not allowed hire an agent, take money for flights/visits, hire any kind of handlers and so on. Basically you have to pay your own way and be your own everything. Once you hire someone you are ineligible to play for the NCAA (men's basketball). These rules slightly change from year to year but this sums it up.