Is it permissible for a university student to use the scholarship and aid designated for their studies for Hajj, in exchange for taking out a student loan to cover their study expenses?

If the granting entity stipulates that the aid must be spent on studies, then the condition must be adhered to. If it does not stipulate that, then it is permissible to spend it on whatever permissible things one wishes or to save it for Hajj, provided that the loan is not usurious. It is not advisable to take out a loan for Hajj, and it is not permissible to take out a loan if there is no hope of repayment. However, it is preferable not to take out a loan if there is another way.