Dear Student ,
Coming to your second question at first that the electric field between two charged plates is uniform and non zero or not?
Now look in order to store some charge one must put a constant, uniform and non zero electric field between two charged plates of a of a parallel plate capacitor .
Now answer of the first question is the electric field between two capacitor plates depends on the (1) surface charge density and (2) dielectric constant in C.G.S . As , Electric field between two parallel charged plates is , .
Now as the surface charge density increases then the electric field intensity also increases and when the dielectric constant's value increases the electric field decreases .
But in S.I system , the electric field between two charged plates is ,
So here also as the surface charge density increases the electric field increases and when the the product of dielectric constant and free space permittivity increases the electric field decreases .
Regards