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Could you tell me how to properly express these and how to grammatically say them please?

PAST

I would have preferred that he had done that rather than having gone out
I would have preferred to have done that (rather) than gone out.

PRESENT

I would prefer to go out rather than stay home.
I would prefer that we went/go out rather than stay/stayed home

Is this grammatical?

1 Would you rather I came to pick you up but didn't do the dishes or did the dishes and didn't pick you up?

Thank you
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Your past examples are correct, though they might not really be called the simple past. The second of your present sentences needs to be like this:

I would prefer that we go out rather than stay home.

The last could be well expressed like this:

Would you rather I came to pick you up, but didn't the dishes, or would you rather I did the dishes but not pick you up.

It sounds better wtihout the tense marker at the end.
Comments  
Thank you so much

but wouldn't it be

Would you rather I came to pick you up, but didn't the dishes, or would you rather I did the dishes but not picked you up./ didn't pick you up

I had one more question please?

How would you properly say these if they aren't already correct?

1 I preferred to play the game than to watch the movie which is why I didn't watch the movie.

2 Why didn't you go? I just preferred to stay home rather than go out./I just preferred staying home to going out; that's why.

Thank you Englishmaven