would rather

Hi people!

First of all, I'd like to know whether my assumption is correct: When we begin a sentence with "I'd rather you...", should a verb in the simple past tense follow?

E.g:

I'd rather you didn't do that. (This sounds as expressing annoyance, doesn't it?)

I'd rather you sat on the corner.

What if we want to use the past perfect?

E.g, "I'd rather you hadn't talked so much at the party"* I think this one is incorrect, because we should say: "I wish you hadn't talked so much at the party."

Furthermore, if we want to ask a question about someone's preference, can we say "I was thinking of going out tonight but would you rather stay at home?"

Thanks a lot!

Mara.