The biggest assumption is that, to first order, the number of asteroids and comets hitting the Earth and the Moon was the same as for Mercury, Venus, and Mars. The bottom line is that the more craters one sees, the older the surface is.
This can be interpreted in two ways: why it is important to know the age of a planet or how is age dating important in determining the age of a planet?
It does burn in oxygen, and if you can pass the combusted gas through limewater, the carbon dioxide will turn the limewater milky by producing calcium carbonate.
Once the half life of an isotope and its decay path are known, it is possible to use the radioactive decay for dating the substance (rock) it belongs to, by measuring the amount of parent and daughter contained in the sample.
An important point is that we must have an idea of how much of the daughter isotope was in the sample before the decay started.
We can get absolute ages only if we have rocks from that surface.
For others, all we are doing is getting a relative age, using things like the formation of craters and other features on a surface.