u/IndependenceNo9027

I'm going to give examples to clarify my question:

"I appreciate YOUR/YOU taking the time to write to me."

"HIS/HIM doing that was a surprise to us all."

"THEIR/THEM leaving suddenly caused major issues."

"It could be interpreted as HIS/HIM being simply uncomfortable."

"Are you okay with MY/ME doing the job alone?"

Well, you get the idea - so which one is grammatically correct in those situations, the possessive article - such as "his" - or the pronoun in accusative (?) form - such as "him"? Does it perhaps depend on the verb? I'm not a native English speaker, but I speak English fluently, so I feel like I should know this, yet I still don't. Can anyone help me with this?

Thanks for any answers!