Mary wants to go to university if she passes her exams.
- this is correct when not specifying a university. Adding 'the' simply narrows where she wants to go study.
Does Brad like eating fish? or Does Brad like to eat fish?
- either way is correct, as long as Brad has chips with his fish. :) In this case either form of the verb is acceptable and commonly used. The word 'eating' describes the action while 'to eat' is the action instead so when asking if Brad likes the action it is interchangeable.