You don’t normally ‘open up’ a door, a window, or a book. You could open up a shop, or a counter for business, in which case it means the same as just ‘open’. ‘Can’ and ‘could’ are independent of ‘open’, and in practice are often interchangeable : ‘Can you open the window’ and. ‘Could you open the window’ are equivalent, and neither is actually a question or refers to ability to do it ; they are simply requests to do it. In other contexts ‘can’ and ‘could’ may refer to the possibility of an event, or ability to carry out a task, etc. ‘Can the door be opened ?’ asks if it is possible, and ‘Could the door have swung open ?’ asks if this could have happened. Use of ‘can’ and ‘could’ in English is variable and understanding of how it is used has to be learned from experience.

Agree with Thomas in general with a caveat: as an English speaker (American), we say "open the door" but Ive never heard anyone say "open up the door." "open up" usually means conceptually something that could be taken apart: a box, a room, or even a person. A door just opens. But do other English speakers use it in this way?

No, either can or could goes with either one. The difference between can and could is just present tense versus conditional (puedes vs podrias). Open up just adds some emphasis to open. "Open the door" and "Open up the door" mean the same things but there is more urgency to the second phrase. Sometimes when a person shares personal information you could say, "he opened up" and you would not say, "He opened." But, generally the two are interchangeable. Hope that helps.