Is it permissible for a university student who is subjected to injustice and denied deserved grades, especially foreign students, to deal with a professor there who accepts gifts in exchange for helping foreign students succeed, knowing that the student may be confident in their answer and yet be surprised by failure?

If a student fears harm and injustice from a teacher, and that they will fail if they do not offer a bribe, then there is no sin upon them for offering it. This is because what is given to obtain a right or ward off injustice is not considered a bribe. Rather, a bribe is what is given to invalidate a right or establish falsehood. It has been reported from Ibn Mas'ud and a group of Tabi'in that it is permissible for a person to offer something to protect themselves and their property if they fear injustice.