If you actually do mind, it wouldn’t be sufficient to say “Yes”. Yes, I do mind. Yes, in fact I do mind. Note also that “do you mind?” has a different use as well. If I’m talking and someone interrupts me, for example, I could say “Do you mind?” (I was talking and I’m annoyed that you interrupted me. I want you to stop talking so that I can finish.)

Logically, the correct answer is “no, go ahead” because the actual question was “do you mind?”. I think that is the better answer. But in real life, you will hear both versions of the answer.

"No" would be the correct answer because it means "I don't mind" or "I don't care". You will often hear people responding "Yes" colloquially, but it can be confusing as saying "yes" means that it would bother you.

No, go ahead is correct. But I would say not at all, go ahead.

Either answer is correct. Do you mind? No, go ahead. May I borrow your pen? Yes, go ahead.