No they don't. You use the same hub to hub model as airlines. E.g London to Edinburgh, not London to Edinburgh stopping in 4 places.
One of the nice things about traveling at night is you have less time pressure and congestion so when doing track repairs it's usually fine to divert the train.
Yup. These two points are not an issue at all, and are in fact strengths for sleeper trains. Being able to redirect a sleeper train without any (or minimal) impact on its timetable is a big plus.
Usually they depart from the last boarding station around midnight, and the first disembarking station won't be hit until six in the morning. Some outliers exist, but the number of people getting on or off there is negligible. For most travellers you are in the train before 22:00, and won't leave before 6:00.
Yes, you can get off in Nürnberg at 4:08. But almost no one does that. The train just happens to have a halt there¹, but 95% of the passengers get on in the Netherlands and the Ruhr Area, and won't get off until Austria (and vice versa).
What do you mean? Changing the train consist during the trip? That is exactly what they can do.
Hamburg/Amsterdam on one end, Innsbruck/Wien on the other. Those wagons get shuffled about like a deck of cards en route! So in Amsterdam there is one train with wagons marked Wien and wagons marked Innsbruck. You get in the right numbered wagon, and end up where you want. In the middle of the night, in the middle of nowhere (actually, probably München) they turn two trains into two different trains.
Where I live it's a pretty common feature of train timetables - certain trains will split partway through a journey, and no-one gets off in the process (well, unless part of the train is terminating at the stop)
One of the nice things about traveling at night is you have less time pressure and congestion so when doing track repairs it's usually fine to divert the train.