A rather strange idea I must say. So the thing is that the area where the water is open, so it's the same water outside as inside. I would be happy to hear your thoughts about it!
If this structure would be lowered into water with normal air pressure inside the box the water would compress the air a lot and water would fill most of the space inside. To keep the level of water at a level of 10-15 % of the height of the box it wouldn't be possible to lower it more than about 1.8 meters with normal air pressure in the box. Therefore, there is a over pressure inside the box and more air had to be filled into the box as it was lowered down to the bottom. By increasing the pressure of air inside the box it would also keep the box from imploding because of the surrounding water. A human can survive at a higher pressure, at least for a while: "Depending on how you go about going that far below water and the specific tolerances of your body a deadly depth can be from 500 to 1200 feet." ([link]
) Imagine that it's not as deep as 500 feet. Rather a few hundred feet's or maybe less, but that is not really important.
To get food he has to fish, which you notice if you look closely. The small propellers provides the lamps with energy. The water is moving and makes the propellers spin.
The big failure will probably be that the air runs out as it would require a lot more trees to keep producing enough oxygen to keep him alive. Slow death in the aqua custodia.