In OP's context, the only difference is that could/would you [do something]? is slightly more polite and/or "deferential" than can/will you [do it]?
The reason for this is simply could/would (and might) are verb forms more strongly associated with hypothetical scenarios. So using them places more "distance" between the speaker and whatever he's asking for. There's more on the issue in this question on ELU, and if you're prepared to read a bit more, have a look at this excellent answer to a closely-related question.
Re OP's point about could being a "past tense", I'd say that from some perspectives English doesn't really have a "past tense" anyway. What it has, particularly with modal verbs like can, may, must, shall, will is verb forms that often refer to the past, but can also refer to anything that's not here, now, present.
Thus if I say "I could do it yesterday, and I can still do it today", could references past time (before the present) and can references the present. But if I say "But I couldn't do it again without help", could [not] references either a future time (after the present), or a hypothetical time ("away" from the present), depending on how you want to look at it.