Your district "cap" is 1 district per 2 pop beyond the first pop, since your city center functions as a district. So at 3, 5, 7, 9, 11, etc you unlock the ability build an additional district. The Aqueduct and Neighborhood don't count towards this cap, and you can build multiple Neighborhoods. Otherwise, yes, the main limiter on districts is finding suitable places to put them. Note that the non-Housing, non-Amenities districts get boosted production for every set of two adjacent districts, so there's some strong incentive to cluster your districts (although they do scale up faster in the presence of things they like, so the district bonus is more of a "this city's map doesn't favor this district" thing).
Also, make sure to place your Industrial (Production) Districts and Entertainment (Amenities) Districts such that multiple City Centers are within 6 tiles of them, as their 2nd and 3rd tier buildings extend their bonuses to any city within 6 tiles, which is a strong stacking boost.
With the scaling costs of Builders/Settlers/Districts/etc, Production is at a premium this Civ. Especially if you want to win by science without chopping every tree on the planet. Stupid space shit takes so much production.
Been wanting to try to set-up an 8 city (two-concentric circles, outer one rotated 45degress, minimum settle-distance apart) wheel to try to maximize those 6-tile bonus overlaps, but my maps are all either contorted land-masses that don't give enough room, have mountains/luxuries fucking up the arrangement, or don't have enough fresh water around to make it work smoothly during set-up.
High Population is good, but nowhere near as good as it was in Civ 5. You only get ~0.7 science production per population, vs the upwards of 2/pop for Civ5. Specialists also have kinda poop conversion rate, and having to hunt down more amenities to support higher pops is irritating. I doubt it'll be optimal to gun for huge pop cities this game like it was with the Tradition Science stuff in Civ 5. It is still probably important to get a cluster of 4 (to benefit from the civic that increases your farms output for each adjacent farm) Farms in your "core" Cities to help you reach mid-level population.