GIVE ANSWERS - English

May I is more polite, and is asking for permission to do something. Could I is informal and is asking if you have the ability to do something.

first of all, MAY is a present tense and COULD is a past tense.
MAY (or might, if in the past) is more polite and most likely when you ask permission - in a polite way.
CAN (or could, if in past tense) - its a permission as well, but usually means that you are ABLE to do something, you are capable of.
Exemple: I can speak English/Can I come in?
May I come in? May I use your phone? I might use your phone if you let me.

May I, is use in when you want to be not only poly but also you are asking if there is the possibility you can do it, could i is use in the way that if you can actually do it or not the action, i mean if you have the capacity to do it