I'm gonna explain the difference between 'could' and 'can' ! Most of the time it is clear from the context, but use of" can" can also express possibility (rather than ability). For example, giving advice answering the question: How can/could I improve my English? You can/could listen to the radio, watch TV and read the newspaper. You could listen to the radio emphasizes that this is a suggestion or piece of advice, whereas You can listen to the radio emphasizes simply that this is an option that's available. You could listen to the radio contains more personal involvement and subjectivity; You can listen to the radio is more strictly factual and objective. Similarly, How could I improve my English? is more a request for advice, whereas How can I improve my English? is more a factual question about available options. Really hope this helps!

You can use any of them when making a request, but "may" is the clearest and most formal, because it asks for permission. "Can" refers to current ability; "could" is about the possibility of something happening soon. Which means you might get the following smart-alec answer: Q: Can I have a glass of water? A: Hmmm... well there's a jug of water... some glasses... so yes, you can. (long pause) OH do you WANT a glass of water?? Same for "could". But I think most people will be kind and give you water instead of taking your sentence literally. ;)

Ok, look here: May I open the window? - you ask, if someone against opening it; Can I open the window? - you are interesting, if you are able to open it; 'Could' is 'Can' in the past. Could you open the window yesterday?, but Can you open the window now? I think, that's all.

May I and could I are formal words which show some respect but 'can I' is used for conversation between same age people...

Excellent answer, Anna! Also, the three words can be used for asking for and giving permission. E.g., May/Could/Can I have a glass of water, please? May is more formal than could and could is more formal than can.