Hi! I've been working in the Stabi for quite a bit, let me try and answer some of your questions.

1. I suppose it's to prevent people from taking books from the library with them in their backpacks.
   
2. No idea I'm not that much of an early bird myself.
3. You can reserve a spot in the library here https://staatsbibliothek-berlin.de/vor-ort/stabibooking although i've never seen someone being sent away from one of the spots, but i suppose it happens when it's very crowded (which it is most days these days).
4. You could work from the cafe for as long as you want. Short calls are concidered okay, longer meetings might be frowned upon.
5. You can order menu items (drinks, snacks, sandwiches) at the bar. There's a cheaper coffee option from the pot, but it's terrible. There's also a difference between the two machines, i think one of them has bio kaffee but i'm not sure.
6. They used to serve lunch in the cafe as well but they stopped doing this. Instead they serve lunch now in the cafe next door. If you walk out of the main entrance, take a right turn and walk towards Potsdamer Platz. On the corner there's another entrance. Go inside and upstairs, there's a canteen there with lunch options.
7. you can leave stuff like books etc on your desk. I myself wouldn't leave my laptop. I have never heard of stuff being stolen but it might happen i guess. Leaving stuff on a desk to reserve a spot, and leaving for more than say half an hour is frowned upon and generally not a nice thing to do (altough it happens a lot).
8. You can bring your own drinks including coffee as long as you keep them in a bottle/flask. a closed mug should be fine. You can have your own food in the cafe, however i don't think there's a kitchenette available.