When do I use “can” & “could”?
In a company, the HR asked me:
"Could you please sign here".
I want to know whether it is correct or "Can " should be used or simply "Please sign here" is sufficient.
When to ideally use Could.
Strictly logically speaking, asking "Can you sign here?" would be sufficiently answered by "yes" with no further action required. "Yes, I am able to." However, we generally understand that as a request in English, so we'll say "Yes" and sign. (I think in Russian, it's more common to use the imperative: "Sign here, please", and if you say "Can you sign here?" they'll say "of course" in a surprised way, but then do it anyway).
Anyway, saying "Could you please sign here?" instead is just a way to make the sentence more polite by making it less direct. The same happens in French - instead of saying "I want a cheese sandwich" at a restaurant (je veux), you say "I would like a cheese sandwich" (je voudrais) - again using the conditional, similar to English.
So, both are socially correct, the latter is more polite, and technically speaking you can say "Yes," do nothing, and look like a douche.