Korean Question (compound verbs vs auxiliary verbs)

I don’t know the difficulty of this question (if only Korean natives could answer or not and I am typing in English)

I am pretty sure auxiliary verbs is a western thing but I was just wondering the extent of the usage of
어/아 버리다 (finish up/end up with, emotional nuance)
어/아 주다 (do for someone)
어/아 가/오다 (the continuation into the past or future)
어/아 내 나다 (express completion different nuances between the two)
Idk if is an auxiliary verb 어/아다니다 (to continually do something (habitually))
어아 지다 (become or passive modifier)
어아보다 (to try make an effort to do something)
-can these be added to any verb if the context allows for it?
-And what is the difference between auxiliary verbs like the ones above and examples like those below (I’m pretty sure these are fixed and cant be modified?)
compound verbs (examples)
날아다니다 (to frolic)
뛰놀다 (to fly around)
쳐들어가다 (to invade)
these verbs are they’re own free standing entities or are they made from these auxiliaries verbs
들다 갈다 these verbs are used in compound verbs but form my knowledge don’t have any auxiliary meaning separate from their original meaning

Also compound verbs are made from adding 어아 서 but without the 서. How is the difference known from an auxiliary verb being added to a base verb and this 어아 and then verb meaning?
The only thing that comes to mind is that you cant just add 어/아 버리다/어/아 주다 things like this to whatever verb? (even if context allows for their suffix usage)
I know verbs like (to forget) mostly uses 어/아 버리다 and (to help) uses 어/아 주다 in a lot of cases.

  1. can 어아보다/어/아 주다 be added to any verb if context allows for it or are they only allowed to attach to certain ones?

  2. are compound verbs made up on the spot by combining to verbs or are they preset and every Korean speaker knows them as they’re own words?

  3. How to know the difference between these two
    어아 가다 (the auxiliary suffix that expresses continually into the future)
    어아가다 (to express the movement after the verb that is in the compound verb)

I was curious about compound verbs as well generally because they are difficult to look up and its hard to know if they mean literally what they mean or if it has a more abstract type of meaning. For example 사가다 could mean buy and leave/go or it could have a different type of meaning and those variations but the more complex ones. I was wondering if there is a list somewhere to avoid the dictionary look up problem.