I think they forage for food during the night.
They can pick food out of the dish...but they can't swallow it until they get back into the water.
Sleep?...I think you got it. They don't have an extended time like mammals do.
I don't know about the air thing. Whenever I checked on them in the winter..they were laying on the bottom of the tank..motionless.
One interesting thing I learned. The females can store the sperm from the males for over years and still lay fertilized eggs. Three years is the max recorded.
https://video.nest.com/live/4Lc0WbToTr