What is the ruling on a father's intercession to admit his son into an institute by paying money, how does one repent from that, and what is the ruling on benefiting from scholarship funds?

Success in the exam is a condition for joining the institute, and you are not entitled to join it as long as you have not succeeded, especially if that leads to depriving someone who deserves to enter. Intercession (wasta) in general is not permissible if it results in depriving those who are more deserving and entitled, and this is confirmed in scholarships and academic institutes. If intercession leads to depriving someone who is more qualified and deserving of a job or study, then it is forbidden and unjust. However, if it does not lead to the loss of anyone's right, then it is permissible. Schools and institutes are public facilities, so if intercession results in depriving someone who is more deserving in terms of eligibility, then the intercession is prohibited. If your leaving the seat results in it being occupied by someone who deserves it, then leave it for them; otherwise, complete your studies, seek God's forgiveness, and repent. As for the scholarship amount, refuse it to absolve yourself of responsibility, unless the state or ministry grants the institute's director legal authority in that matter.