Is it unlawful for a student to receive an enabling grade after supplicating to God, following a hint from his professor about Ph.D. exam questions, and what should he do?

What you have mentioned is permissible, and you will not incur sin because of it. It does not affect your testimony or your studies. So, abandon the whispers of doubt that come to you. What you did is neither cheating nor an infringement on the rights of others. Some teachers may advise students to focus on specific lessons because the questions will come from them, and there is no harm in this. We advise you to ignore these whispers.