Ing vs infinitve in detail

Hello there

Few questions about infinitve vs ing

Please verify these. Bit detailed. Thank you.

1. Can we use participles as adverbial modifiers or just as adjective modifiers?

2. Participle are adjective but infinitve can only be adjective modifier not adjectives themselves

3. As verbs object

We use Infinitive (when idea is abstract or depends on main verb) and gerund when the idea is real or coexists with main verb
Now as per couple of articles and a book
Infinitive works as noun if verb is non action verb/answers 'what' eg. want or like Works as Adverb if verb is an action verb/answers 'why how when to what extent'Eg. Study.
Question Gerunds are nouns. So gerund should only be used after non action verb/that answers what. Since gerunds or ing cannot work as adverbial modifiers.But this is not the case as gerunds are used after many action verbs answering why which when how ie as adverbial modifiers. Thus confused?
Or maybe my idea of action verbs is wrong, it can answer 'what' Ie. we can use gerunds after action verbs answering what but not after verbs that answer why when how etc. Right.In summary what+futue event/unreal infinitve as noun, why when how +fuure event infinitve adverbial modifiers and what+ real or coexists use gerunds but cant use gerunds after verbs puspise or how why when.
4. As adjective modifier after noun or objective pronouns. Should we use same guidelines that we use while deciding verbs object ie. If (real, complete) use participles adjective modifier else if ( abstract, unreal or provides a purpose) use infinitve adjective modifier

Eg. Willingness to achieve or i told him to future and if it would be present or real use participles correct?

5. Also Should we use same guidelines while deciding subject complements

Eg. My desire was to become a doctor(provides a purpose)
What i hate is becoming a doctor (real ie. Not futue event)

Am i thing in the right direction?

6. And with reduced relative clause. Use same guidelines?

Thanks you so much in advance