So you have two choices:
Not after midnight.
Not until midnight.
After: later than something; following something in time
Until : up to the point in time or the event mentioned
If you say "Not after", you are saying that the restaurant doesn't close later than midnight. It could close any time before midnight, so you haven't answered the question "What time does the restaurant close?". You have said when it doesn't close.
If you say "Not until", you are saying that the restaurant doesn't close up to the time of midnight, then at midnight, it closes. That does answer the question "What time does the restaurant close?".
I believe I understand your concern because similar confusion arose at some point in my English study, too, due to a linguistic difference between my native tongue and English. Your language is perhaps like mine, Thai, where you answer to the truth condition of the statement of the question rather than the truth itself. For example, if you ask, in Thai, "aren't you going to school today?" and the answer is "yes," the answerer means they are not going to school. "Yes" here is "yes, (it is true that I am not going to school)," not "yes, (I'm going to school.)"
I think it helps if you think of English as somewhat simpler than that. In English, whether you answer "yes" or "no" only depends on the reality and has nothing to do with how the question is worded. Whether the question is "do you know?" or "don't you know?," "yes" and "no" still have the same meanings: in both cases, if you answer "yes," it means "you know," and if you answer "no," it means "you don't know."
Answering with plain "yes" or "no," however, may sound too flat and could sometimes be misunderstood, so it's safer to respond with a complete answer like "yes, I do." (meaning, you know) or "no, I don't" (meaning, you don't know) if you can't think of anything fancier like "no, I never knew," or "no, this is the first time I've heard about it!"
As stated by other Answerers, one thing to consider is that sometimes "don't you know?" is a rhetorical question, meaning the speaker doesn't actually expect an answer, so you don't have to answer them. You usually can guess from context whether it is an actual question or not.
Best Answer
The original question is:
The question refers to a specific instance of time. It's not referring to you yourself. Hence the correct answer would be:
Here you're saying that it indeed is the first time you've been to Britain. Note again that it points back to time, and not to you.
Now, just to make things clearer.
This answer points to you (yourself) traveling to Britain, and not a specific instance of time. So, the ideal question to this would be:
Now, the same question can also be replied in the negative, if you haven't traveled to Britain before. Then you reply something similar to your sentence 1(with a slight modification):
And lastly:
The use of "am" suggests a present, continuous action; something that is happening now (present tense). So, this would be a proper response to: