correct response

[sitifan]

Ivy: Do you know whether they catch the fish all year round?
Bruce: __________________________________.
(A) No, they don't. (B) Yes, I do. They don't catch the fish all year round.

I think option B is correct. Am I right?

[Barb_D]

When someone asks "Do you know if..." the person is NOT wondering whether you actually know. If you don't know, you say so. If you do know, you don't just say "Yes, I do know that." You also usually omit saying that you do know, because by giving the answer, you have clearly shown that you know.

Either say you don't know, or just answer the question.

A: Do you know what time it is?
B: Yes, I do. --- This is an unacceptable answer by courtesy, regardless of grammar.
B: No, I'm sorry, I don't. -- This is fine. You can't give information you don't have.
B: It's 5:10 pm. Sure, it's 5:10 pm. Yes, it's 5:10 pm. -- You can say "Yes" or "Sure" but you don't say "Yes, I do know."

So in your example, it's completely unnatural to say "Yes, I do."

[emsr2d2]

My grandfather (and my father, actually) always reply to questions literally, just to make a point.

Me: Dad, do you know what the capital of Azerbaijan is?
Dad: Yes thanks.

Me: Granddad, do you know what time it is?
Granddad: Yes, I do. [It's time you bought a watch!]

My family? Sarcastic? I don't know what you mean!

[sitifan]

My family? Sarcastic? I don't know what you mean!

I don't know what the sentences in red mean. Would anyone please explain them to me?

[emsr2d2]

I don't know what the sentences in red mean. Would anyone please explain them to me?

Apologies. I was being sarcastic myself. What it means is that given the post I made, it appears that my family (especially my father and grandfather) are very sarcastic people. Actually, that is true.

However, to be sarcastic, my "My family? Sarcastic? I don't know what you mean!" would be the reply I would give to someone who read my original post and actually said to me "It sounds like your family are quite sarcastic!"

The truthful response to that would be "Yes, they are". My sarcastic response is the one I gave and which has caused you confusion, for which I apologise.

Sarcasm is probably the most difficult part of language to comprehend and it can be very region-specific. The British are particularly keen on it. Some British people are even good at it.