I'm not sure about them all, I'll just pick a few I'm fairly comfortable about:
Korea: Science boost is like an RA completing. It applies to scientific buildings in the capital. No relationship with natural wonders.
Polynesia: Disembarkation ends the movement, just like for anybody else, as you already guessed. Interesting with Polynesia is to look for ruins on remote islands with units like archers and chariots. If they find weapons you can have a very early longbow or knight. Any civ can luck out like this, but with Polynesia's ability the chance is just much bigger.
Siam: Yes, the Wat gives all the benefits from a university.
Aztec floating gardens: Just lakes, not salt water. And it doesn't stack with a lighthouse, like you would expect. Well, you would expect that once you know a lighthouse gives a food bonus to all water tiles, salt or sweet. But so that doesn't work if the lake is already boosted by floating gardens.
The 15% more food applies to the gross food, not the net, so that's strong.