Plants and algae are constantly converting carbon dioxide to oxygen (and sugar) using water and sunlight. This more than makes up for the oxygen they use to stay alive; the extra oxygen is what we rely on to breathe.

But just because of the size of the Earth and the atmosphere, it would take a long time for any changes to propagate through it. This also means that any attempts to fix a problem with the atmosphere (like excess carbon dioxide) would also take a long time to take effect.

It did take hundreds of millions of years to form. When Earth first formed 4.5 billion years ago there were just a carbon dioxide and nitrogen atmosphere. Then about 3.5 billion years ago the earliest oxygen producing microorganisms came about and we started getting a trickle of oxygen in the atmosphere generated by combining water, carbon dioxide and sunlight. But levels were still low until about 850 million years ago when the oxygen levels in the atmosphere shot up and most of the carbon dioxide was converted to oxygen and organisms. This was right about when the first plants developed, and we started getting multicellular organisms. Since then the plants have been able to maintain current oxygen levels. Or at least somewhere between 15% and 35%. Without plants we would not have oxygen.

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It isn't completely constant over geologic time. Earth's oxygen has been as low as 0 and as high as about 33% at different points during Earth's history.

The oxygen in the air is the result of an equilibrium between plants and other photosynthetic organisms (it's actually mostly microbes in the ocean) producing oxygen as a by-product of photosynthesis. This equilibrium is pretty stable, since organisms are short-lived and organisms will be slightly more successful in environments that are more favorable to them. (As an example, global plant growth has accelerated pretty significantly as humans have added carbon to the atmosphere, although not by enough to compensate for the rate at which we're adding it.) This part is basically a closed cycle: plants produce oxygen in the process of capturing carbon to use in their "bodies", animals eat the plants and burn the plants' "bodies" with oxygen from the air.

Over the very long term, though, there's another important effect: geology. Or more specifically, geology driven by living things. Earth is old enough, and living things dominant enough in its surface chemistry, that life on Earth and Earth's own geology are intimately linked over the longest timescales. (This is, I think, incredibly cool. In a very real sense, the very stones of Earth are part of the biosphere.)

In the processes described above, some organisms manage to die and decompose without returning their carbon to the atmosphere. The corresponding oxygen that was liberated during the capture of that carbon, then, ends up sticking around in the atmosphere over the long term. This is, in effect, what happened during the burying of the organic material that became fossil fuels, and it's part of why the era in which those fuels were produced had the highest oxygen levels in the history of Earth to date.

On the other hand, sometimes geological processes expose this buried carbon to the atmosphere, where it reacts with oxygen. This is the same kind of chemical cycle as the regular biological one, just dominated by geological processes over much, much longer times.

There are a few other minor contributors, like serpentization of certain rocks, but the ones described above are the big drivers.

The net effect of all of this in the Earth we have today is very close to zero if you ignore humans. So, human activity aside, Earth's oxygen levels aren't changing quickly over any timescale remotely relevant to humanity.

But thanks to the fact that we're burning an absolute ton of buried carbon (effectively accelerating one side of the geological processes described above), the oxygen content of the atmosphere has very slightly declined due to human activity. Not by anything significant - a few parts in 10,000 - but some.

Both. There are quadrillions of tons of atmosphere on Earth and it's composition doesn't change over night. At the same time, most plants and algae will absorb CO2 and release oxygen. They'd also absorb oxygen but most plants need the extra carbon more than they need the spare oxygen. Mind, this only works so long as we aren't destroying plants and algae while simultaneously dumping CO2 into the atmosphere.

It takes millions of years to change. The amount of O2 in the atmosphere is large compared to the amount of organic carbon in the biosphere and the available fossil fuels, so burning the biosphere (trees mostly) and fossil fuels don't change the amount of O2 that much.

Over millions of years, oxygen oxidize metals and carbons brought by volcanoes and then exposed through erosion, so oxygen level can go down. This is opposed by having living beings producing organic carbon-rich sediments that becomes rocks under water. Though a small percentage of those rocks are coal, most of it don't contain enough carbon to be fossil fuel or are too deep under ground.

Over millions of year the oxygen level change. It is believed it peaked at some 30% in earlier times. Also, it has been close to 0% for billion of years (it took a long time for oxygen produced by life to oxidize all the already available metals, mostly iron).

The amount of CO2 changes fast because there is very little CO2 naturally in the atmosphere. That's because CO2 is very soluble in water and also combine easily with ions such as calcium ions to make carbonated rocks. So over million of years, CO2 in the atmosphere doesn't change much even though O2 changes a lot. If you include the CO2 in the ocean and the carbonated rocks then it changes a lot. That's also why we say that the CO2 we put in the atmosphere will last about 100 years. If we were to stop putting more CO2 in the atmosphere, it would go down to its previous levels by the ocean absorbing the CO2 in about 100 years.