It has nothing to do with the tense. After modal verbs and auxiliary verbs, you always use the infinitive of the verb. Only the first verb changes for person or time. He can SWIM She should ARRIVE on time. He will HAVE been living here for 5 years by then. She doesn't LIKE him. He didn't GO to university.

Yes, Lupita, it is because time is concrete and we have to use have in her or her. That is a perfect time.

Yes, the same.

Yes.

If we understood correctly this is what you intend to convey “he must have been playing 90 minutes when game finishes”. Sorry if this is not what you try to convey. Thanks.