Unlike Chinese, this question should be taken literally in English. Most commonly if someone asks, they might be wondering if you have eaten yet, and if you want to eat together. It is probably not an offer to feed you.

"Have you had lunch?" is the same as "Did you eat lunch?" You can say, "Yes, I had lunch." or "Yes, I ate lunch." OR "No, I didn't have lunch." or "No, I didn't eat lunch."

If you've had lunch, say 'yes'. If you haven't, say 'no'.

breakfast

This question isn't used as a greeting in English like in Chinese, so there's no reason not to answer truthfully. When English speakers ask this, they mean it literally and genuinely want to know the answer.