If a father objects to all marriages to any suitable men for his daughter until she receives her PhD, and she is in need of marriage, is the daughter still required his consent to marry? Do you have any advice for this daughter? Would it be permissible for her to do mutah with a suitable man until she receives her PhD, which then she will tell her father about getting married to him?

If he refuses to let her marry any person, even if the proposer is decent and faithful, and staying unmarried is posing big difficulties for her, then in this situation she doesn’t need his permission to do a marriage contract.

My recommendation is to pressure her father to agree to her getting married. Let her mobilize many people to talk to him. Doing Mut’ah may cause her difficulties later if her family or community finds out. It could negatively affect her standing and reputation, so from this aspect I would not recommend it.