This feels like a great setup for a West Marches type campaign. Every session is a different foray into the Night Districts - with different characters involved. A larger meta-plot can be brewing, but doesn't have to be...This is intentional - I want that each foray is against the clock, and since likely running this using D&D 5e have that there is not time for a long rest during a trip to the Night Districts. There will be faction and other issues thatr happen purely on the "daylight city" (which is there full time) that will allow adventures of varying length.
Interesting and undefined. Can the residents of the Night Districts cross the gates to a day district? Can they survive sunlight? I was already planning that some districts kept the gatges locks and guarded during the night (so leaving them or going to them at night requires dealing with that) and others have a freer interface. I picture some inhabitants as tricksey and fey in the mythical and not-so-nice term, like the Goblin Market of Christina Rossetti's poem of the same name, but still able to be bargained and deals made.
For about the same reason we don't send a squad of knights into a fairie ring.
There are tall walls, with gates between the day districts, so then they will be between the day districts and the Night Districts. (I keep tripping on the term "day districts" - they are actually full time districts, available at day or night. Hmm, I wonder if one of the secrets of the city is that there actually is also a hidden Day District, that only exists during the day.