Seems like insane prisoners do all the normal stuff, but they can't use standard cells.
According to the description any prisoners with the Hyper-Active reputation move faster when they're triggered (suppression or lack of psychiatric treatment). Conversely any with the Depressed rep will move slowly. Not sure how it works if they have both - maybe they're bipolar or maybe the two reps would cancel each other out?
I converted one of the ready-made prisons and have 291 insane prisoners. Several have the Insomnia reputation but 100% of inmates still have a Sleep need. The individual profiles show that on average insomniacs sleep for about 5-15% of the time while others sleep for around 20-25%. In practice an insomniac might stay up all night before building his Sleep need and then crashing the following night.
It would sometimes be handy to be able to code a room for several security categories, but it is already possible to make this work. Just add several doors into the main room, build a small lobby room in front of each door and then code each lobby for a different category. You can also just split the regime so that different categories use areas (canteen, yard, showers, etc) at different times.