High or low in a room; It makes no difference where you put the detector -- but not because carbon monoxide and air have approximately the same density. Both are gases and as a result, diffusion alone and the entropy effect will take care of mixing them. Any convection currents and/or forced-air turbulence present will also enable the gases to mix and affect the detector.
It is popularly misconceived that light (low-density) gases will somehow float atop heavy (higher density) gases. Indeed, if the higher density gas was admitted low in the room, and done so in a manner that would not cause much mixing, it would take a while for the gases to become thoroughly mixed by the mechanisms mentioned above. Even so, they would eventually mix. I run a ceiling fan in the bedroom nightly so the air is mixed well. I have my detector near floor. My heat vents are in the ceiling (part of the A/C ; If you have heat registers on the floor, it might make a small difference, but because of the mixing that goes on, it is highly unlikely that the detector requires a specific location.
I cannot say for certain because apparently it slowly uses itself up as it measures the air; however, I can say that my first purchase of a similar model lasted about 7 years before it began to beep and tell me that I needed to replace it.
We used to have propane on the farm for 37 years, and I believe the answer is yes. Anytime you burn a furnace from a 'fuel' not electric, there is a chance of carbon monoxide...just like the exhaust from a car.