Which state of matter is highly compressible, is made of particles moving independently of each other, andis present in large quantities near earths surface?

The highly compressible state of a matter is its gaseous state. The gaseous molecules are highly compressible due to presence of maximum space between the molecules than the other state of the same material. As for example the gaseous form of water that is vapor has the maximum space between the H₂O molecules and lowest in the solid state that is ice.

 The motion of the particle have some postulates which is called the kinetic theory of gas. The gaseous particles of any particular gas can move independently in the vessel in which it is kept. The motion of the gas in a vessel is described by the Brownian motion.

The gaseous state of the material like carbon di-oxide (CO₂), oxygen (O₂), nitrogen (N₂) remains nearest to the earth surface which is stratosphere.  

oxygen, selenium, tellurium, and polonium.

they're all from the same group as sulfur (group 16).