Every school year I've had has begun in late August or early September and ended in May or early June, with a single semester taking between 4 and 5 months unless it's a summer "semester", for which the schedules are more compressed to fit in 3 months or 6 or 8 weeks. (The reason for summers off dates back to the once-common use of children for labor on their parents' farms in the summer.) If you want more precision than that before diving in, check the schedules of the college in question or ask someone who works there. The schedule and calendar for each semester are widely publicized at least a whole semester ahead of time, if not two or more.

I don't know of any college that doesn't require payment at the beginning of the semester rather than at the end, so what you want would seem to require that cause and effect happen in the wrong order (first the payment, then the determination of the grade). Is having the student pay at first, then you reimbursing later if the condition is met, not an option? The only other thing I can think of then would be an escrow service. People most often think of escrow in terms of mortgages, but all it really is is some third (or fourth) party that holds money until everything is settled between the original parties. It just so happens that mortgages are the usual circumstance in which escrow service is used. There are contracts involved, but an escrow service is very familiar with them and handles them routinely for the job, so it would have standard procedures to make the process as efficient as it can be for their own good. The catch is that they might require a certain minimum amount of money to be involved before they'll do it and the cost of a class might not be enough, or they might demand a fee that is unacceptably high.