She might have been waiting for us.
Here, perfect "have" is a plain (infinitive) form.
"Have" is the perfect auxiliary and "been" is the progressive auxiliary.
The modal "might" is a tensed form and "waiting" is a lexical verb.
I strongly recommend dropping the term 'helping verb'. It's nonsense
The phrase "have done" also carries a special meanign of "to be finished with" or "to stop. See this Collins entrty This sense is also used as "have done with", for example "I have done with you. Do not come here again."
So "She hopes to have done." can mean "she hoped to be totally finished." ...