thermodynamics - How is $frac{dQ}{T}$ measure of randomness of system?

I am studying entropy and its hard for me to catch up what exactly is entropy.

Many articles and books write that entropy is the measure of randomness or disorder of the system. They say when a gas system is let expand the randomness increases etc. But they end up saying $\frac{\mathrm dQ}{T}$ is the measure of increase in randomness and is called the entropy.

Even if I believe that entropy is the measure of randomness of the system I don't understand:

1. How does $\frac{\mathrm dQ}{T}$ hold the information about the randomness of the system?


2. How is entropy independent property of any system. I suppose that any two parameter in the equation $PV=nRT$ should completely describe the system. Why would we need entropy?

Thank you.