I'm surprised he didn't question how the link between the characters and the avatars worked. Everything else seemed plausible enough, but I struggled to find an explanation for this. Any thoughts?
So, we at least know it wasn't AT&T.
On the other hand, once you have floating mountains, the science has gone out the window.
If this type of appendage evolved early enough, then all of the descendants with a common ancestry could maintain a common communication link. This would have had to evolve very early to be shared between both plants and animals, but I suppose it's conceivable if you can imagine plants with a nervous system. Another possibility is that there is a strong mechanism for genetic transfer between different species and kingdoms (maybe very flexible retroviruses or unseen genetic engineering), but then you might expect to see more shared features between plants and animals.
The part that I didn't understand why why the Na'vi would always be the "masters" in the link with the other animals (it seemed more peer-to-peer in the link with the trees).
Perhaps because they're best able to hypothesize, in the same way that we train our animals rather than the other way around...although I'm less sure of that when it comes to cats.
I'm less sure of that when it comes to most humans. Their animals seem to train them, not the other way around.
As for the link not being peer-to-peer, it might be as simple as the bigger/more complex nervous system dominating the other one.
You could potentially have motile plants (maybe going directly from free-floating algae to something that swims). But generally, plants are stationary or move passively on Earth because they just don't have the energy. Animals hoover up many times their weight in plants over a year so they can do stuff like intentional motion.
This can't be true: Not all plants are autotrophic, and not all autotrophic organisms are plants.
As for the autotrophic non-plants -- I guess you are referring to algae and some bacteria?