Rico And The Correlatives
Yes, I intentionally tried to make the title sound like the name of a band.
Perhaps you are seeing something that I am not, but I’m not sure the correlative και...και construction here is anything unusual or noteworthy. Different correlatives have different meanings, but this one seems to imply a slightly closer coupling between the items in the correlative than just a straight και joining them might give you. Any exegetical significance to this? Not that I can see, but who knows.
As for the further examples, as noted some are the same pattern and some are not. I would think the τε...και constructions would be the closest structural parallel, rather than the ου/μη μονον...αλλα και and other constructions, though those are at least semantically somewhat parallel.
If you want more examples of a και...και correlative construction, BDAG has a very brief entry on it. See page 495, entry 1.f.
So what does the passage mean? It means that Timothy needs to persevere in true teaching, otherwise the salvation of himself and his hearers is in jeapordy. For Paul here, for a teacher to teach error he endagers himself. In such a case the listener has no access to truth, and so they too are put in danger.