3: Do they exercise, and if so, what do they do? How often?
Nothing Nero does can really be straight-up called ‘exercise’. A black hole’s metabolism is designed to store everything and expel or expend nothing and so trying to use up what one has eaten is counterproductive as well as ineffective. The only thing exerting oneself would do is prompt Hungering, which is a state most black holes, including Nero, dislike going through.
4: What would they do if they needed to make dinner but the kitchen was busy?
In the hypothetical situation where Nero would entertain a being who requires prepared foods there would be no such thing as a busy kitchen. Such a thing would take place on a planet Nero has taken over and serves him, and as such the kitchens as well as all their staff would freely be at his disposal. Backtalking would only add to the meal served - meat is meat regardless of its origin.
5: Cleanliness habits (personal, workspace, etc.)
Black holes are self-cleaning. Though the skin (and the clothing) acts as a barrier between the abyss inside and the outside world, anything that comes in contact with them is slowly absorbed. Even traces of a dip in a pool of mud would disappear in few minutes, less with concentration. Nero does make sure to erase such traces quickly though. He dislikes clutter, as everything that exists only has the right to exist if it has a purpose.