How is air quality related to weather?

The number 27 bus from Peterborough is not related to the weather

As air pressure pressure decreases with altitude, so does the densite of air.

Yes, because meteorologists use a barometer which measures atmospheric air pressure and a barometer is a weather instrument so air pressure is part of the weather

Only insofar as water is a compound of hydrogen and oxygen and these two gases make up a part of the air.

Yes, that is why a barometer is used to predict the weather - low pressure increases the likelihood of a storm, whereas high pressure means that it should stay dry