Re: Sleeping on the Enterprise
We saw the crew in the their quarters some times so that would be off duty/sleeping time for them. When something important was happening then the bridge crew would get recalled. That's why Kirk would be called to the bridge some times when he was in his quarters or taking a physical.
And frequently when he just happened to have his shirt off.
“All the universe or nothingness. Which shall it be, Passworthy? Which shall it be?”