Question

Subject-auxiliary inversions not associated with questions

Answer 1

A. helping verbs
Have, has, had, having are what kind of words 

"To have" is a modal. Both modals and be verbs are called auxiliary verbs. 
Examples of modals: have, may, shall, can
Be verbs: be, am, is, are

Auxiliary verbs are  also called helping verbs. They are non-action verbs that only serve as a support to the main verb. Hence, they need ACTION VERBS. For example, we say "She HAVE dreamed about unicorns." and "We ARE eating the food our mother made." "Have" and "are" are auxiliary verbs helping the action verbs "dreamed" and "eating".