When you apply for asylum, you are given an immediate removal order. However, this order is stayed/suspended till you get a final decision. If the decision is negative, as in your son's case, the order becomes active and he has 15 days to leave Canada. This is just part of the refugee process.
CBSA can legally show up to remove him at any time after those 15 days. This does not usually happen; they don't just break your door down and deport you.. but they can.
Yes, you can apply for judicial review to the Federal Court, but this is NOT a guaranteed right of appeal. It's asking the Court for permission to appear before them and have them review the case. The FC may well refuse to review the case.
If the study permit was granted on the basis of the pending refugee claim, then yes, it will be cancelled and he will have to leave Canada. Your lawyer is the best person to give you advice based on your specific circumstances.