Mine ventilation would be a superb feature. Mines have huge networks of shafts to try to get air to the miners. Dwarves could even carry animals to check for toxic gas. A bigger issue is all those furnaces indoors; they should suffocate everybody and put themselves out without proper chimneys and air access. As for invaders getting in, dwarves could use grilles, slippery walls, steep drops and other defences to reduce the chance of that.
How much air a dwarf needs would just be a base figure and maybe some increases based on physical activity, though I would suggest ignoring that at first. Areas could have a "breathable air" fraction of the total air, which creatures, fires, and furnaces would convert into "non breathable air". If the fraction of non breathable air got too high, anything (except undead and other possessed beings) in the tile would suffocate and die. Plants (of the photosynthetic sort, not mushrooms like plump helmet) would turn non breathable air into breathable air. Ratios of breathable to non breathable would equalise over time if given access. While this might massively increase load, it would be very satisfying to see old forts suffocate once dwarves realised that they could not respire with an atmosphere of mostly carbon dioxide.
What do you mean by "hardcore"? It should just be logical.
That would give chimneys a duel function, not only do they allow smoke out they also allow air in, both of them securely. The thing we have to be careful of here is making the system too complex and thus FPS destroying. We should probably not try to positively keep track of oxygen levels, instead we should model stale air and smoke as gas clouds emitted by creatures or fires periodically.
Stale air and smoke are both are produced by fires, creatures on the other hand produce only stale air. Stale air does not represent C02, instead it represents the relative lack of oxygen. Stale air and smoke emitted by fires start off as a high temperature, which causes it to rise upwards if at all possible, unlike the stale air emitted by creatures.
Both types of clouds automatically dissipate if they reach the surface. They try to spread as widely as possible, so that there is an even distribution of stale air or smoke, while if hot they also try to move upwards. Cold smoke gradually diminishes and deposits soot onto the group as it does so, which can then be cleaned up by dwarves but stale air can go away by going to the surface. Smoke and stale air are both deadly to creatures that need to breathe, but the former has a more violent way of operating.
Since they constantly equalise into the surface, which always has 0 smoke or stale air the clouds will always dissapear as long as there is an access to the surface.