Ex: I got used to your being here.
1. How would this sentence be parsed?
got [main verb]
used to [adjectival]
your being here [gerundival phrase]
2. Is 'used to' a prepositional verb?
No. Got is the verb. Used to is adjectival. Cf. I am used to...
3. How does 'here', which is an adverb, modify 'being', which is a gerund (noun)?
Gerunds are "verbal" nouns, meaning they have verbal qualities. So, they can indeed be modified by adverbs. The adverb here modifies the gerund being. We know it's an adverb because it answers the question Where?
4. What if 'your' was replaced with 'you', would the obect of 'to' be a fused participle of you and being?
Sorry. I don't understand your question. You is the object of used to in this sentence:
Ex: I got used to you being here.
And, in turn, being here modifies you.