The sudden release of gas will push other gases out of the way, that is true. But in a closed system like a keg where there is no mixing, you will not see stratification of the gases, they mix evenly. And let's be clear, a CO2 extinguisher does not need to push all of the O2 out of the space - the atmosphere is ~21% O2. The amount of O2 required for sustained combustion varies by material, but in general people throw around the number 14% O2 to sustain burning. So the CO2 extinguisher only needs to get rid of 1/3 of the O2. For breathing, we collapse when the O2 level drops below ~8%, and suffocate in minutes if it is below ~5%. More importantly, CO2 levels above 5% cause problems, with immediate loss of consciousness somewhere above that (10%? 15%? I'm not sure). So again, not all of the O2 and other gases need to be evacuated from the space to be dangerous.
that's why a balloon filled with helium rises.
You might have posted pre-coffee, but you know this has nothing to do with what we're talking about.
Gases mix - the molecules move constantly (if the temperature is above absolute zero), and they move faster the warmer it is. There is so much space between molecules and they so rarely interact with each other that we can effectively say they do not interact. Given time and no stirring there will be an even distribution of each type of molecule throughout the given space.
It is not an oil/water analogy. It is blue water vs. yellow water. You can layer them as gently and carefully as you want in a closed container, but given time you will end up with green water.