Undecided questions
해주다 / 애준다 の違いはなんですか？　Are these just a formal and spoken form of "Have ~ done"?

I think you wanted to ask about the difference between 해주다 / 해준다.
first of all, "해 주다" means "somebody does it instead of somebody else".
and it is the form of a verb root (infinitive?).
"해 준다" means the same thing but we say this like "내가 이걸 너에게 해준다... 라고 할 경우에는 말야...". -> "Let's say if I do this to you...then..." -> google trans "私がこれをあなたにしてくれる...とする場合には、..."
I don't think we say "해 준다" much in the ordinary conversation except for my example...
maybe somebody else here could answer more...

해 주다, 해주다(both are correct) - infinitive form of the verb
해 준다, 해준다 - present tense of the verb. -ㄴ다 is used after the verb to show the present tense, like 가다 - 간다, 오다 - 온다, etc.

I guess it might be "-해주다/-해준다"^^'

"verb stem + -아/어/여/해 주다(-てくれる/あげる)" can mean "to do sth for sb" , "to do sb a favor" or "to give sb sth" (literally), and
(sth = something, sb = somebody)

"verb stem + -(ㄴ/는)다" can be used....
1. when sth happens regularly or always
그는 매일 그녀에게 키스해 준다. (해 주다 + ㄴ/는 다 ☞ 해 준다)
= He GIVES her a kiss EVERYDAY.

그는 언제나 내 부탁을 들어 준다.
= He ALWAYS doES me a favor.

2. as a narrative form in a play or documentary film to explain to audience what is happening now with a narrator's voice.

3. as the present progressive
그는 지금 잔다. (to sleep = 자다, 자다 + ㄴ/는다 ☞ 잔다)
= 그는 지금 자고 있다.
= He IS sleepING NOW


\^o^/