[Buddhaheart]

I got used to your being here.

1. How would this sentence be parsed?

A simple declarative statement (sentence) in which:
I: the subject
got: main verb
used: adjective, characterizing the subject ‘I’
to: preposition, joining the noun phrase ‘your being here’ to the adjective ‘used’
your being here: noun phrase, object of the sentence
your: pronoun
being: gerund
here: as an adjective (not adverb), modifying the gerund ‘being’. It’sused here for emphasis; as an adverb, modifying the verbal aspect of the gerund.

2. Is 'used to' a prepositional verb? See 1. above.

3. How does 'here', which is an adverb, modify 'being', which is a gerund (noun)? See 1. above.

4. What if 'your' was replaced with 'you', would the object of 'to' be a fused participle of you and being? You can’t. It would become ungrammatical as ‘being’ is a gerund (verbal noun), it must be preceded by the possessive form of the pronoun ‘your’ and not ‘you’.