About "compound phrases", when do you use "noun + noun", and when do you use "adj. + noun"？

For example： (noun + noun)
◆ a conversation problem
◆ language acquisition
◆ comfort zone

There are adjectives for "conversation", "language" and "comfort", then why do not you say：
◆ a conversational problem
◆ linguistic acquisition
◆ comforting/comfortable zone

vise versa (adj. + n), why do not you say "parent supervision" rather then "parental supervision"？

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If there is a new concept I want to express, say "Problems at schools", which expression is safer? School Problems or Scholastic Problems？

Honestly, I think it's usually just random, but sometimes there is a small difference.

"comfort zone" is an example of "because that's just how we say it". Logically I suppose you could say "comfortable zone" ("comforting zone" wouldn't mean the same thing), but it's an idiomatic phrase and so you can't say "comfortable zone" and communicate the same thing. "language/linguistic acquisition" is the same in that that's just how we say it — plus, "linguistic acquisition" is a bit vague because you can acquire a linguistic ability without acquiring a language. "conversation problem" sounds weird to me and I would always say "conversational problem".

Oftentimes a compound noun is more "specific" than an "adj + noun" compound. For example, an "education program" is not always the same thing as an "educational program". An "education program" is a program specifically about education, so about grading, lesson outcomes, classroom management, etc. An "educational program" is a program that educates people, such as one that teaches people a new language, but could also refer to a program about education itself and how to properly educate people. For example, you can have an "educational program" for a summer camp that involves teaching children how to speak Spanish, but it isn't an "education program" because it isn't about the process of education itself.

This is an incredibly long answer but my point is that often, the way we say it is just how we say it and there's no deeper reason than "just because". Sometimes there is a semantic reason why, but a lot of compound phrases are coined a certain way, and then they're only ever used that way, for no reason other than because that's how the phrase was originally invented. I unfortunately can't explain how to decide which to use if you're trying to make a new compound phrase, but often, if there's a common-enough associated adjective, using the adjective will be acceptable.

As for your "problems at school" question, it would only ever be "school problems". "scholastic" is an uncommon word in the first place, and additionally, "scholastic" often has the connotation of being about education that takes places within a school rather than just everything to do with a school. Students being bullied is not a scholastic problem, but it certainly is a school problem, for example.