For sure they ADRed everything where the camera was actually flying (opening scene, fight scene, for example). I think a lot of it was just using the camera, not the actual drone.
This is so rad. I will, however, point out that he has like 19 other things you'd need to pull this shot off that I haven't got outside of the 1 thing I have got, tape.
I was pitching a commercial to a tropical resort and had to spend a week training myself on underwater shooting. I was lucky enough to have an expensive Nauticam Rig for my 5D. Housings like that are, as you suggested, slightly heavier than neutral buouancy and make all the difference. They also have gears to adjust focus or even zoom, which is super helpful. But yeah, learning to focus under water is a trick. Probably the biggest lesson I learned was how to move your body. Having forward movement works or any kind of intentional movement, that way you're not trying to stabilize yourself in the water while keeping a camera still. It also helped that besides already being scuba certified, I was trained in freediving a month earlier and was able to stay down, without a tank for a minute or two. I did this whole little test without scuba stuff.
One last helpful thing on exposure: depending on where you are relative to the surface, remember that it's very dark below you and very dark above you, so if you follow motion from down to up or vice versa, the exposure changes dramatically. Generally I over exposed for the shadows because the white streaks of the sun just felt dreamy to me, but you don't want it all to blow out.
Here's my results from the tests: https://vimeo.com/140104214