1.Mary wants to go to university if she passes her exams. = Its perfect how you have wrote it. Its correct without ''the'' If you had included '''the'' it would sound strange. 2.Does Brad like eating fish? or Does Brad like to eat fish? = They are both correct but it would be more natural to simple say ''Does Brad like fish?'' It would be understood by the context that you are referring to eating fish..

'to university' is a british form, here in the states we add "the" but in the case you asked about we here in the usa would say 'a' university if we're not specifying a particular univ

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.