When they were talking about Professors named after a bush. You might be thinking of Professor Ivy, which was an anime exclusive character. And I think they named her Ivy, because the only professor at the time was Oak. And both can be related if they are poison ivy and oak.
Kukui and Hala are both trees. They are trees in Hawaii. Not only is Kukui a tree, it is also the state tree of Hawaii. This makes every main game exclusive professor names after a tree.
Lunaala was definitely outside. There is a sky where it pops up. So this might be a throw back to 2nd Gen where we can catch both legendary pokemon within the games.
One thing I didn't hear them mention, is the fact that you could see most of the island in a few camera angles.
And although he might have been sarcastic. I highly doubt there is only 1 gym and they change with seasons. Not only is there only 4 seasons, but the idea is honestly, probably one of the dumbest ideas I have ever heard in a pokemon game. Possibly even dumber than Pokemon Fusion. It would take 4 months to get 4 badges. Not to mention Hawaii is mainly tropical, unless you are up in the mountains.
As for Poke Mart and Poke Centers, I hope they keep together. But I hope it is set up more like the Unova ones.
It was fun to listen, but some things were cringe worthy to me lol.