Just to be clear, and I really looked in the in-game civipedia and couldn't find it:
a) you get 1 district per 3 pop, NOT including city center and aquaduct, but can build 2 at start? So 2, until pop 6?
b) if you have a replacement district, such as the Germans, Greeks, and Russians, building that doesn't count towards the cap
These are questions, not reports.
I wish the city build screen would tell you how many districts you can still build and so forth. If it does, I can't see where.