Door to the hallway or sliding door?

In your case, I would definitely not have the door open into the room, as it also protrudes into the room at a relatively narrow spot. Towards the hallway, it doesn't bother visually at all, probably looks good. Will there be a wall at the end of the stairs?

Yes, that is closed and the staircase is most likely closed as well (e.g. reinforced concrete stairs).

No lamp connection in the kitchen and only one lamp connection in the hallway? Isn’t that too dark?

I temporarily removed the light from the kitchen when moving the kitchen around – it was in the way. The kitchen lighting should definitely cover all work surfaces. Above the peninsula probably something like a pendant light. Certainly lighting in the cooktop area, if not on the island, as well, and whether a general lighting is still needed – I don’t know. So far, only one lamp outlet was planned in the hallway (you can hang more than one lamp on it). Maybe two outlets in parallel wiring could be made there, yes...