RIP Nintendo Power

[Mutsukki]

And obviously the 2 DS ones had the same Link.

Actually, Phantom Hourglass is the same Link as Wind Waker. Spirit Train is a sequel to Phantom Hourglass, but with a different Link (you get to see Niko from Wind Waker as 100+ years old man, the only human character to ever survive seeing another Link). The rest is right though (Oracles and Ages are the same Link and timeline).

There's also a few other characters who have had reincarnations despite not being connected to the Triforce. Epona and Tingle are probably the most notable.

Yeah, there are a lot of characters who go over, besides the main ones. The entire Tetra Pirates crew were part of the Hyrule Royal family (as seen in Minish Cap and a painting in Wind Waker), for example. Queen Rutela may be Ruto's equivalent in Twilight Princess and so on.