Is this a difference in American/British English or did I learn it wrong?

I am a Brit and would choose option B - "Haven't" in both cases. I suspect this is the same in the US but I am sure others will clarify that.

The correct answer is B. "Didn't you see X lately" is weird. "Haven't you seen X lately" is normal.

I agree with you completely. These other commenters didnt read your post correctly. To me, neither of the options fit in this context. Either 'you' needs to be the first word in the sentence or the contractions should be changed to "have not" and "did not". In either case though, using "have" is the right answer

Haven’t is the correct use. Haven’t you seen indicates a period of time that started in the past, while didn’t you see much of them, indicates a present state. Since we are talking about “lately” it’s a period of time that started in the past and continues presently. I hope that makes sense.

for the second question, to my ear it seems wrong. "You haven't seen much of them lately then, eh?" is what I would say. (yes for the record I'm Canadian 😂) "Haven't you" makes it sound like a question, when in reality it's more of a statement until you hit the "then" Re: haven't vs didn't - haven't is still correct. "Did you see your parents" implies one action in the past; "haven't you seen" implies multiple (recent) visits in the past

I don't understand how you can be halfway through the season but most teams have only played 1/3rd of their games. they're just going to cram 2/3rds of their games into a half a season?

I'd go with 1B For 2 they both sound wrong, but B sounds less wrong I'd say Have you not seen much of them lately? Haven't you seen much of them lately sounds really off. It makes it sound like the speaker knows for a fact that they've been seeing the parents and is questioning what the other person said.

For what it is worth, option B sounds weird to me. "Have you not seen much of them lately, then?" Would make more sense to me, because it fits the context of the leading line better. Unless I'm misreading something?

This seem like hard questions for C1. B is more common but I think there are some dialects that might say A, and that first question similarly, B is more correct but I can definitely imagine someone saying A.

Since I didn't see anyone answer your question about why not "you haven't see much of them lately, then?", I'll add this. Questions in English are commonly formed with inversion, meaning you switch the position of the subject and the verb. If you get rid of the "then" in this sentence it is just a statement, and with the "then", it sounds more like a leading statement than a question. It sounds like you already know the answer and are trying to get the other person to acknowledge/agree with you. The way the answers are worded don't sound sarcastic or like you've seen your parents too much. They sound like genuine questions. Albeit, the answers as written sound a little clunky. As a native speaker, I would probably reply, "Haven't you seen them much lately?" https://en.m.wikipedia.org/wiki/Subject%E2%80%93auxiliary_inversion Here's a link to the grammar rule if you want to learn more!

Q1: I would pick B. Q2: I would pick B. USA

Do and Have mean different things. ‘Have’ is part of the “present perfect simple” and ‘do’ is not. Remember that the “n’t” means NOT. So it isn’t a positive question. It’s not sarcastic either, it’s just a question. One person just said they have to remember to call their parents so they can mention the upcoming trip. Their friend then poses a hypothesis that they have not seen their parents, since they still need to tell them about the trip. The friend does not assume, but guesses. This is called a close ended question vs an open ended one, because it only requires a yes/no answer.

The first example uses American grammar with a British example, which is interesting.

I’d answer q1 with B and q2 with B. Neither question or response have been phrased particularly well- imo. With reference to a question you asked in the comments about it being sarcasm. Unless it specifically asks about the meaning behind the question, or the intent the question is supposed to convey, I’d assume that they are not being sarcastic, ironic or humorous in any of the questions- even when they read that way. Are you being tested on colloquial language ie how we use it in everyday speech or grammatically correct language- the Queens/ kings English? The most obvious is American English is more informal and tends to drop excess words where it’s possible. American English has lexical differences as well as differences in nouns. The word meaning is sometimes different to English when spoken compared to English usage elsewhere in the world. There are no syntax differences between English and American English and grammatically the difference is mainly seen in the use of singular/ plural nouns and in the way proper nouns and plural verbs are used.

B certainly is the answer I would choose. As far as sarcasm/accusation goes, I'd need more context to make that call. In my experience both 'haven't' & 'didn't' are used to question a statement without making an outright accusation. 'Haven't' makes the query a little more gentle.

Look in the top left corner of the page. It says present perfect simple. I’m going to say that the answer in the book is probably B. In my context: “haven’t you seen enough of them lately?” Would express that the speaker thinks the listener has seen a lot of their parents. British English.

I know this wasn’t OP’s question, but the first question annoys me. It clearly says the PL season is halfway over, and yet both answer choices say the teams have only played a third of their games! Someone must do something about this. (Also it’s laughable to imagine Manchester United leading the Premier League)

I agree the correct verb is “haven’t”. However, to focus on your specific question, no I do not think the phrasing with the verb fronted in the question makes it seem sarcastic in any way. I do not see any implication that “you” have seen your parents a lot. To give that impression, the question would need to be something like: “Haven’t you seen a lot of them lately, then?” I think the sticking point is the construction “much of them”. This is an example of “much of a something” but used in the negative. In this sort of construction, the meaning of the phrase expresses a lack of something (or an inability). The other oddity in “Haven’t you seen much of them lately, then?”, is the tag question of “…, then”. Here, I think it is best to understand the “then” as a confirmation of understand as to causation. To me the meaning of the question is something like: “Is that because you have not seen your parents very much lately?” Or, maybe, “So that means you have not see your parents very much lately, right?”

I don't like the phrasing of that sentence. The additional "then" feels weird to me, I can't tell if that's just a British way of phrasing or something.

Have you not seen much of them lately, then? Would be the correct response. Did not implies that we are strictly speaking about the present, while have not includes past to present. This is my understanding as a native speaker.

"Didn't" would refer only to the past, which wouldn't work with "lately." So B would be correct, with phrasing that is definitely British. In the US we'd be more likely to say something like, "Have you not seen them much lately?" or "Have you not talked to them much lately?"

Oh dear, that first question has aged poorly 😓 For the second question, I believe option B is correct