Are the fees imposed by some foreign universities for reviewing a student's application considered permissible, given that these fees are non-refundable in case of rejection and are considered a down payment towards registration fees in case of acceptance?

The questioner mentioned that the money is for the effort of studying the file, and they take it in return for their effort. If the student is accepted, they consider it part of the fees, but if not, they do not waive it and take it in return for the effort they expended in studying the student's file. Therefore, there appears to be nothing in Islamic law to prevent this.