For example:

Q: May I turn on the TV?

A: Yes, you can. / No, you can't.

Yes, you could. / No, you couldn't.

Yes, you may. / No, you may not.

Yes, of course you can.

Yes, of course you could.

Yes, of course you may.

No, I'm afraid you can't.

No, I'm afraid you couldn't.

No, I'm afraid you may not.

Can we use "can" or "could" to answer questions begin with "may"? Please give me your opinion, thank you!
Properly no, but it is very common in spoken English.
I agree that "can" is a common type of response, but not "could." That would sound very odd to me.
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'May' and 'can' are virtually interchangeable in common everyday speech, much to the dismay of the first grade teachers of all the older members here. 'Could' shouldn't be used in the answers.

'Could' is often used in the question of request: could you please turn the radio down? Could I offer you some fresh lemonade? Could you tell everyone that dinner is ready? 'Please' is always, of course, a nice addition.
Thank you all! Your replies simply cleared all my doubt.
ViceidolThank you all! Your replies simply cleared all my doubt.
A student asks, "Can I go to the restroom?"

The teacher jokingly replied, "Yes, you can, but I won't allow you to go." ('you can' here means 'you are able to'.)

The above shows that 'may' is the better word.
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Hi Viceidol,

May I turn on the TV?

Of course.
Why not?
No way!
I'm afraid not...

So you can leave out the verb, and that's what most people would do, I think. If you want to repeat the verb, you could say "you can / can't". I think "may" in the answer would be so rare that it might even sound really odd. It's already pretty rare in questions, actually... Emotion: smile