[MrPedantic]

I would agree that your sentences are fine, and that a possessive pronoun can appear before a gerund.

1. Do you mind my smoking?

— note that this can mean either "do you mind if I smoke?" or "do you mind the fact that I am smoking?"

It would also be idiomatic to say:

2a. I don't mind you coming late.
3a. Do you remember him getting into trouble with the police?
6a. I hate them borrowing money from us.
7a. She is afraid of him leaving her alone.
8a. Do you mind my asking? = do you mind me asking?

Best wishes,

MrP