I hope it works out! I am naturally blanking on any examples I might have in mind, but I know there exists at least one case where I prefer adaptation to original for similar reasons of it being better-rounded, more complex, more humane.

I mean, they might improve some things while making others worse. The Game of Thrones TV series has massively salvaged the shitty pacing of the later novels, but they've also managed to make the plot even more rapey than it was in the original. So who knows what the overall balance will end up being. But the WoT pacing problems almost have to be improved by adaptation (it's hard to see how they could be made worse), and not having the interior monologues of the characters means the show writers would have to go out of their way to replicate a lot of the things that annoyed me on a character level, because they'd have to put them in dialogue instead.

What is the relation of the world and its mythology to our own?

The implicit idea is that our own world is somewhere else along the curve of the Wheel, which is why those echoes appear -- we're the extremely distant past and/or future of what you see in the series. If you dig too deeply into that cosmology a lot of unanswered and possibly unanswerable questions appear, but as a basic conceit it works.