I want to know the how many people can live on Earth's oxygen. Is there a point when humans would use up all the oxygen? What would be the limiting factors? Given we have charts to show the rate of growth, can we predict the date Earth will reach maximum capacity? Has anyone put a hard number on this with facts to back it up?
Way, way, more than we could ever feed.
First, no one has put a hard number on the number of people the Earth could support purely based on oxygen consumption. This is because we'd run into food and clean water problems long before we hit an oxygen ceiling.
It was nicely put in this article about Earth's oxygen reserves:
Simply put, our atmosphere is endowed with such an enormous reserve of this gas that even if we were to burn all our fossil fuel reserves, all our trees, and all the organic matter stored in soils, we would use up only a few percent of the available O2. No matter how foolishly we treat our environmental heritage, we simply don't have the capacity to put more than a small dent in our O2 supply.
Basically, we will never be able to keep enough humans on the planet alive long enough to be in danger of running out of oxygen.
If you're mostly interested in the maximum number of humans the Earth could support based on food supply alone, estimates range from 10 billion to 40 billion on the high end. Some estimates say we're already past the Earth's carrying capacity. Of course, humans are trying (and will always try) to intervene and save themselves, so estimates without intervention are non-existent.
There are also some nice answers here given a question with a fairly different set of assumptions.
Those humans have to eat. That means we grow things for them--and the oxygen you breathe to metabolize the food is less than the oxygen the plant produced while growing that food. (Passing it through animals in the process doesn't change this basic pattern.)
You will eventually reach the point where the energy of the light that grows those plants becomes too great and we roast but we will never hit an oxygen limit.
Note that even if we assume synthesized food we get the same result. Food is mostly carbon, hydrogen and oxygen. Hydrogen and oxygen are water, the carbon will have to be obtained from atmospheric carbon dioxide--but that will release the oxygen the same as if the plants did it.