This answer comes as a counter-proposal answer to @nhahtdh's.
Let me first state my fundamental viewpoint: If we allow these questions to be asked without using anime as context, we open the door to all kinds of off-topic questions. Everything from programming to outdoor living becomes on-topic. And that's... bad.
Following the policy Logan M suggested, these questions would be off-topic
This is incorrect. The anime cited in these questions (well, at least three of them) is required to give the question context.
Take, for example, Why strike stones taken from inside a pot against each other?. If we remove all references to the anime, we get:
I saw someone taking two stones from a pot, and striking them against each other. What does it mean? Is it some kind of supernatural belief?
For all we know, it could be starting a fire with two blocks of flint. The environment, actions, and characters present in the scene are necessary to answer it. Even if you saw someone doing this in real life, you wouldn't have the context of the son leaving home.
Contrast with Check and circle marks in test papers, and you get:
I came across a test paper containing someone's score. However, it is interesting to note that the correct answers are circled while the wrong ones are ticked (checked?). As far as I know, ticks are for correct answers and circles are for incorrect answers (unless I've been living in a shell, which would be embarrassing).
The person who wrote this intentionally placed an incorrect answer for question #1. As you can see, it is checked while the rest are circled. Does this mirror how Japan marks the test papers of students? If so, why?
Aside from the possible lacking context that this is happening in Japan, nothing changes. It is a question about how a test paper is marked, not about anime, nor even about its characters. You could argue that you'd have to know about Keima Katsuragi answering the first one wrong intentionally, so I'm willing to let this one slide with an edit (to show the focus).
However, I think those questions have value on Anime & Manga.SE, since they help viewers better understand the Japanese culture, so they can further appreciate the anime/manga itself
Perhaps this will sound harsh, but why are we tasked with helping people appreciate anime and manga? SO is not asked with helping people appreciate code, Math.SE is not tasked with helping people appreciate math, and so on. While it is fantastic that we can help people understand their favorite anime and manga through our site, it is not our responsibility to sell the medium.
Moreover, it's hard to make the argument that anime is really culturally fulfilling. While some like Uchouten Kazoku will provide more cultural themes, if we judged Japanese culture by anime, we'd not only severely overestimate the amount of lolis in Japan, but also miss out on things that are truly important to their culture. (Kind of like learning about World War II by watching Captain America.)
If they want to understand Japanese culture better, that's up to them. We could also help them better understand Japanese language used in anime and manga by making those kind of questions on-topic, but that would be silly. Instead, any japanese-language questions require context from the anime or manga in order to be answered. ((Good), (Bad))
It would also be more natural for the people who see a certain scene in anime/manga and want to understand what is going on to come here and ask their questions here
Of course. So, come ask about the scene. Describe the characters, atmosphere, and how they relate to what's going on. The anime has to give the question context.
Those topics are at odd with the site scope. However, to understand those references, it is necessary for the answer to draw knowledge from those fields to adequately explain them.
Yes. This is an ongoing problem. We will frequently have questions that require information from the real world, such as this world map question. This is why we have contributors that have varied interests, such as physics, language studies, programming, art, and so on. But, this is not to say that this varied skill base is where we should focus the site. That's a bad idea.
As for your question list, I see some that would be good questions.
Why does [this character] reject [this item] as omiyage (gift)?
Sure! Maybe that character had a specific reason to reject that item.
... Unfortunately, I also saw quite a few that would be bad questions.
Why do the Japanese tie omikuji fortunes to fences and tree limbs?
Absolutely not. This is entirely about Japan, and has nothing to do with anime, even if you found an anime with someone doing it.
And yet, you place some questions in the "disallow" pile that I think are bad for the same reason.
As a visitor from the United States, is it polite or rude for me to bow?
Why is this more off-topic than the one about omijuki? If I rephrased it as Is it rude for visitors from other countries to bow in Japan?, would that be "on-topic"?
If we do not have a policy in place like @Logan's, then we will be forced to accept these questions as on topic:
- Why are pagodas pointy?
(I saw a pagoda in an anime. Why is it pointy on top?)
- Why do people drive on the left side of the road?
(In anime, people always drive on the left. Why?)
At this point you're probably thinking that we can just downvote or close the "bad ones". But that leaves us with the issue that the criteria used to select "bad" questions will become entirely subjective. People will say road rules obviously have nothing to do with anime and close it, but anyone who's curious or unsure about what Golden Week is will probably be more than happy to leave it open.
Recall the text of culture that Logan posted above.
Questions about anime and manga in the broader context of Japanese culture.
Asking what Golden Week is, or why a test is scored backwards, is not about anime, nor about manga. (Nor related media.) It is about Japanese culture, or worse, culture in general. It belongs here as much as asking "What's Christmas?" on Movies & TV.
My opinion: We should retain @Logan's policy on the matter. If a question cannot be asked without requiring details or context from an anime, manga, or on-topic medium, the question is off-topic.