Have something done - tenses?

When you use the english expression "to have something done", how can you change it to different tenses?

For example:

"He has his hair cut" <- is this already present perfect, because "has+past participle"

or is "He has had his hair cut" present perfect?

What about present perfect continuous?

"He has been having his hair cut?

or future present perfect

"He will have had his hair cut" or "He will have his hair cut"?

So the questions boils down to whether you have to ignore the "past participle" (here cut) and just change the word "have" or not?

Thank you!