first of all, how would you linguistically call that what I am talking about?

In your subject, you call these things "purpose-clause compound nouns." Strictly speaking, none of these are compound nouns, which in TKD are individual words consisting of multiple nouns. All of your examples may be described as noun phrases, but you can't get more specific when describing all of them. They break down into purpose clauses and genitive phrases.

I have noticed that some words are translated like {pe'meH taj} "cutting knife", while others use -wI': {toSwI' qal'aq} "jungle gym".

And then, sometimes I wondered, why -wI' and not -meH?

Of course, all phrases make sense in both ways, but is there a difference? Why is it not {toSmeH qal'aq} "structure for climbing"? Why say {chevwI' tlhoy'} and not {chevmeH tlhoy'} for "territiorial wall"?
"suntan lotion" is translated as {DIr QanwI' taS} - why not {DIr QanmeH taS}?

What do you think about that?

I think it's arbitrary, and you just have to learn which way it's said. I also think you wouldn't be particularly wrong if you said chevmeH tlhoy' instead of chevwI' tlhoy', for example. It would be like the difference between border wall and wall of the border: one is said and the other isn't, but the other is still perfectly understandable.

Next, I think there is also a difference between combinations where the meH-ed verb directly influences the noun (pe'meH taj means that the knife is for cutting) while other situations are just real noun-noun combinations (as in {nISwI' DaH} which is a "array of disruptors" and not a "array to disrupt").

I'm just lacking the right terms to say what I think, so maybe you can clarify.

Genitive is a broad concept, and Klingon noun-nouns seem to embrace that breadth. You seem to be sensing sub-types of genitive. Here's a page that breaks down various types that appear in Latin: <http://www.csun.edu/~hcfll004/genitive.html>. Klingon grammar treats them all the same.

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SuStel
http://trimboli.name