@AndySanders Something like that mantra used to be true in the early days of MO, but I think you're right it no longer holds water. The more frequently cited mantra these days is "questions should be research level". Now that can mean many things to many people, and the mantra can serve different purposes, some useful, some arguably harmful. But for speculative questions, I think it could mean that the poster should put in some hard thought into the question first. I think my main inner gripe about the original question is that it was lazy, requiring an answer to do a lot of work for the OP.

Unfortunately I don't have a lot of time at the moment, but with regard to the question at main: have you looked at the relevant writings of Colin McLarty? This looks sort of relevant to what you seem to be asking: arxiv.org/abs/1102.1773

Hand-waving about "Grothendieck's approach" does not strike me as "fairly specific". Also the post seems laden with personal opinions like "way too seriously". The third sentence of your meta post sounds like sarcasm; I hope it's not meant seriously. If you're stuck on a problem arising in your research, that might be good for MO, but this question is not (in my opinion it has multiple problems beside those I mentioned).

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Well, I certainly have my strong suspicions who is doing the downvoting on the first, and maybe the third question. It's very likely on the basis of a particular tag, which the user is now scouring looking for things to downvote, in a fit of pique. But since this is speculation, that's all I'll say for now. Just know that we're watching...

"Looks solvable" seems very much in the eye of the beholder, and it may very well be that Z-W Sun had the preamble about three triangular squares in order to suggest that maybe similar techniques apply. The same applies to the first criterion "feels like they have been studied before", although "is looking for a reference" does suggest a possible avenue to improving Z-W Sun's question.

@LSpice There is no actual conflict between Paseman's comment and what one finds on Wikipedia. "Anti-social network" is quoting from an article in the Atlantic, actually a sympathetic portrayal of MO when it was about one year old, and the phrase was meant to suggest a refreshing contrast to "social" networks like FB (Twitter, Reddit, etc.) with their unending discussions, subthreads, arguments, etc.

It's now CW, incidentally.

The answer by Benoît Kloeckner in that Math Edu thread is excellent, and I think you should take it to heart, but the discussion is about something other than what the OP referred to in this discussion is asking about, and so it's a bit of a distraction. I'm disinclined to enter a long discussion about all of this, but I do wonder why you want to weigh in so much on a topic which you admit you have little experience with. MO and MO meta are not there for you (or other non-professional mathematicians) to hone your thinking about your own attempted answers.

I mean, maybe all this is worth thinking about if you're a textbook author, writing for students still struggling with the peculiar ways in which mathematicians use language, but the OP's question was more in view of writing for other mathematicians who are familiar with the peculiarities, and would probably resent such elaborations or over-explanations in a paper. The OP's question is also about naming new concepts, a problem which comes up hardly at all in writing textbooks. Therefore much of this still reads to me as off-topic.

Ooker, I think your last comment is on the right track: however good your advice might be for other areas, I don't think much of it applies well in math. For example, the advice to invent a fictional character (which you even emphasize in a footnote: "Please do this"). For heaven's sake, please don't do this!! Maybe (maybe) John H. Conway could get away with this, because (1) he's a genius, as everyone knows, and because (2) he has a long established record of linguistic whimsy, and people will indulge him. But for those just starting a mathematical career, IMO it sounds like terrible advice.

"Forest" is most definitely not a red herring, in my understanding of how "red herring" is used here: ncatlab.org/nlab/show/red+herring+principle

In particular, I disagreed with everything you said about "forest". That was a case where nothing needs to be done: it's an evocative term already, and widely understood; for that reason your suggestions seem uninformed and way off the mark (and the OP didn't say he had a problem with "forest", did he?). I disagree with what you said about "abelian": it's so commonly understood and entrenched that I know no one but you who has any problem with it. I really dislike the "sabio" suggestion. It's "deja vu", not "de javu". I think the suggestion to use a portmanteau engine is probably a bad one.

This may be for the deleters to answer. But I don't think the reasons given in that Help post were meant to be comprehensive. My own guess is that the deleters felt that your answer was largely opinion-based, not obviously rooted in experience with writing mathematics papers, and indeed arguably gave bad advice for writing mathematics -- to the point it would be better to remove it than leave it there. I myself strongly disagreed with much of it, inasmuch as it purports to do with writing mathematics.

Regarding the requests, the removal of the downvoting utility is a non-starter -- I'm pretty sure that such a request would never be implemented unless StackExchange, Inc. were to change very radically. Your last comment made me laugh, but Asaf was making a valid point: that questions which fare badly at MO should not be automatically shunted off to MSE. But in case it needs saying, this doesn't have any bearing on your question (which I thought was okay).

Marek, I didn't mean to suggest I would support anything you might write, and I wish I were not put in that spot. I meant to suggest that I think it would be fine to ask at meta if your question in that answer-post were suitable for MO (and I see it's been posted as a question and right now has a net score of 3, so we have a partial answer to that question, although I would have left off the paragraph with "Do you agree?"). I agree with others that it would be better not to regard MO as a platform for forming interpersonal relationships -- it's too limited for that.