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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