Regarding your question about being the past tense, they are also used that way. But you also need to make other changes.
Would you like coffee?
This is not about the past. As others have said, this is an offer of coffee. The response is
Yes I would. / No I wouldnât.
(Or any other acceptance of an offer)
Would you have liked coffee?
This is about the past. It means something likeâŚâBefore, is it possible that you wanted coffee?â
Itâs a little tough to explain. But a person might ask that question if invited a friend to a cafĂŠ, got there before the friend, and ordered two teasâŚthen the friend looked disappointed about having a tea. âSorry, do you not like tea? Would you have liked coffee instead?â
The answer here is
Yes I wouldâve. / No I wouldnât have.
Itâs a similar situation for âcouldâ.
Could you take out the trash?
This is a request. As others have said, âwouldâ could also be used as a request here, but itâs not very common (at least like this).
Literally, I think itâs a question of capability. I think âcouldâ means âis it possible for X to happenââŚbut we use it to be a request because of politeness. English speakers donât think about it this way when making a request, but it will help understand what it means in the past.
Could you have taken out the trash?
This is a question about a past capability. It means something likeâŚâBefore, was it possible that you were able to take out the trash?â
Youâd ask this if your kid didnât take out the trash and you want to know if it was possible (with the implication being that you want to know WHY).
The kid would answer
Yes, I couldâve, but âŚ
Or
No, I couldnât have, because âŚ
Or
Not now mom/dad, Iâm playing a game
As you can see, using would/could in the past is possible, but complicated. âShouldâ is also usable in the past.
Should I wear a hat?
⌠Is a question about whether you need a hat (maybe before going outside for a walk).
Should I have worn a hat?
âŚis a question about whether you needed to wear a hat before. Maybe you didnât wear a hat and got a sunburn on your scalp. Ouch! Yes, you shouldâve worn a hat.