"Could you?" or "would you mind?" is more polite and more formal than "can you?" - but as Tracy said, you can add "please" if you use the word "can" to make it more acceptable and polite. We would usually use "can" with someone we know well - a family member or friend; "Can you wash the dishes tonight?". We might use "could you" if you were asking a stranger to do something - "Could you help me with my suitcase, please?" Regarding your last question, it's fine to ask "Can you swim/cook/speak English?" - but you are asking about ability here, not making a request or asking permission. These are all uses of "can". I hope this helps!