The doors are quite small (the two we see in the movies at least, I guess there are more) specially for commerce, and they don't have an easy path (the one after the Balrog goes directly to uneven rocks, stairs and the Bridge of Khazad-dûm, which is very narrow).
Any reasonable city has more than one access road. Even in real life, any sizeable castle even used multiple gates, some made for cart traffic and some not. The only exceptions here are castles built for defensive purposes, but those tend not to be large and/or accommodating a large population.
Air and light: they would need to light everything using fire all the time (or maybe magic lamps?), which would fill everything with smoke as it doesn't seem to have good ventilation but for the doors and the small hole through which light shines in Balin's tomb (is this only for the movie? If they are deep into the mountain the light could not reach there)
Referring back to real life, whale oil was such a valued resource because it burns without smoke. It was the driving factor to create the whaling industry.
Good ventilation also doesn't require a lot of holes if you have reasonable airflow. Given the high ceilings, it's perfectly possible to have airflow above walking level, so it doesn't bother the citizens constantly but the air does move around. This same effect is encountered in houses with higher ceilings and requires little infrastructure to make work. Convection is a very hands-off process.
Note also that the chasms you mention would very much help with creating this convection.
Halls: we barely see a few places; the huge hall with columns, Balin's tomb, the bridge and stairs that are quite narrow and dangerous (no handrails), and some paths and stairs that also don't look very "user friendly". We don't see if there are houses where dwarves lived in, or any other infrastructure with a functional purpose.
Checkhov's gun applies. It wasn't relevant for the story, and therefore there was no reason to visit those locations.
Secondly, not every path would an inner city path where you would expect high density population. To connect to different sides of the mountain, the trails would span much, much wider than the residential areas would. Think of it like a city on a map. It only takes up a part of the region, with a lot of open land surrounding it.
The fellowship traveled along the equivalent of a hiking trail. Not very many houses along those in real life either, and since their only goal was to pass through, there was no reason to dip into residential areas. If you pass through a country, you'd only use the highway, and you wouldn't see much of the country's residential zones either.
Furthermore, it was known to now house undesirables, so the fellowship actually had a reason to actively avoid busy areas that are more hospitable, which explains why the story never visits these areas.
Others: water, plants, garbage... it doesn't look like the best place for them.
Every metropolitan city needs to ferry these things in and out of the city borders. Modern cities are not able to sustain themselves without import of materials and export of waste. Moria would be no different. Especially given their riches, it can be assumed that they had well-funded infrastructure ahead of human cities.
In The Hobbit, it is also explicitly mentioned that Erebor only would be liveable if they could trade with neighboring towns for supplies. The dwarves simply have that much money from a seemingly infinite mine that they are able to spend money to import goods constantly.
It's not a perpetually sustainable business model, but their resources were amply flowing enough that the issue at hand was dragons and balrogs due to overabundance and overmining, not a treasury deficit due to dwindling mining yields.