How does earth maintain a constant level of oxygen?

It doesn’t! the oxygen level of the planet has varied quite dramatically in the last 500 million years ago; as the climate cooled and the land plants died off, oxygen level fell to as low as 12 percent by the beginning of the triassic. Back then, the air at sea level would have felt thinner than at the top of the Alps today.

Burning fossil fuels has reduced oxygen levels very slightly  - about 0.057 percent over the last 30 years. Deforestation only has a small effect because when rainforest is cut down, other plants are usually grown in its place. But it’s marine plankton, rather than trees, that produces about 70 percent of atmospheric oxygen. Global warming will have a significant impact on plankton, which is a much more serious threat to oxygen levels.

If humans became extinct, how long would it take for all traces of us to vanish?

Stonehenge is at least 4,000 years old and still visible today, old and still visible today, and monuments buried nearby could be even older. Most modern buildings aren’t that robust, but some traces would likely remain for at least 10,000 years, even if it was just the magnetic trace of the steel bars inside concrete blocks. When Hong Kong airport was constructed in the 1990s, the island of Chek Lap Kok was flattened and extended, and the straight edge of its northern coastline will be a clue to our civilization for tens of thousands of years. Our atmosphere also has high level of plutonium-239 due to nuclear weapons testing during cold war. This isotope only occurs in nature in incredibly small amounts, and will be detectable as a pollutant for at least 250,000 years.

But the most enduring signs of civilization will probably be deep mines in hard rock, such as South African gold mines Australian lead mines. Here, visiting aliens would be able to see signs of our civilization for millions of years, as the tunnels fill up with sediment washed down by rainwater to create massive industrial ‘fossils’.