Why are partial molar Gibbs energy and Gibbs energy per mol equal?
The key is that the Gibbs free energy is an extensive quantity. This means that for a single-component system it can be written as
$$ G\left(T,P,N\right) = N\cdot g\left(T,P\right) $$
where N is the number of particles and g is the Gibbs free energy per particle. In other words, if you double the number of particles and double the volume (at fixed temperature and pressure), then G will also double. 

From the above expression you can see that the chemical potential is just the Gibb's free energy per particle: 
$$\mu\left(T,P\right) = g\left(T,P\right)$$