About core transformer and ferrites


I have a lot of questions about transformer core : 

1) Here is the typical hysteresis loop of a ferrite core : 

According to me B is the magnetic field stored by the inductor/transformer and H is the magnetic force which is applied on the ferrite. And the slope of the curve represents the permeability of the core. Is is true ? 

H is the magnetic force, but how can I apply this force on my ferrite ? I imagine that the force is created by the current which flows through the windings. Is there a relationship between H and the current ? 

I read that it is important to no saturate the core. If the core is saturated, ie that the core cannot store more magnetic fields ? is this true ? And if the core is saturated, in an SMPS it will destroy the transistor in series ? Why ? If i can't store more energy in my ferrite why is there a problem ? I could say that it will be worse if i could store energy at infini ... However, normally at each cycle end the core should return to the initial starting point (in a push pull topology, about 0 Gauss if we don't take into account retentivity )

What is the magnetizing current or what is the magnetizing inductance ? 

Thank you very much for your help... i m very lost and i will appreciate all your answers ! Have a nice day !