electrostatics - Gauss's Law of Electric Field how it actually works? & How Gauss derived it?

1. 
   

   I want to know how Gauss derived his equation of Electric Field. Did he derive it from Coulomb's law? I don't think so.

   
   


2. 
   

   Please tell me some details about how this law works?

   
   



3. 
   

   inside a Gaussian surface neat $E = 0$ and why it doesn't depend on the shape of the Gaussian surface? (I know, the electric field goes in the Gaussian surface is canceled by those going out of it, but how come it doesn't depend on the shape of that surface?)