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1.-- I would guess that there are several ways to approach this; here's mine:
I - Subject
got - verb
used - predicate adjective
to - preposition
your - possessive adjective
being - gerund (object of preposition)
here - noun complement
2. Is 'used to' a prepositional verb?-- No, it is an adjectival structure; get is an informal copular verb.
3. How does 'here', which is an adverb, modify 'being', which is a gerund (noun)?-- Gerunds keep some of their verbal characteristics, including supporting objects or complements: Being a man is always difficult; Eating too many hamburgers may kill you.
4. What if 'your' was replaced with 'you', would the object of 'to' be a fused participle of you and being?-- You replaces your in casual English. I suppose that then you would be the object of the preposition and being here would be an object complement. This structure (without the possessive) is indeed sometimes called a fused participle.
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