"The source parameter of an earthquake ( like Moment (Mo), stress drop (sigma), source radius (r), Magnitude (Mw) etc.) can be derived simply from the corner frequency of the recorded seismogram". This is not totally true. In first approximation we need of the estimate of the low frequency asymptotic spectral value AND the corner frequency.

Answer to 1) We need of a robust estimate of the spectral content of the waves associated with the (ballistic) earthquake pulse. Corner frequency estimates the source dimensions in simple models (Haskell, Brune)

Answer to 2) No it is incorrect. The spectrum should be corrected for attenuation along the ray path. This can be done in VERY simplistic assumptions if we do not know the attenuation structure of the zone under study

I think you should read a text book. These things are explained. The corner frequency is important because this is the peak of energy radiated (you see this when you consider the power spectrum) and like an antenna radiates best at is own dimension the wave length corresponding the the corner frequency is approximately equal to the source dimension.

The moment can be estimated from the low frequency constant amplitude of the displacement spectrum from the amplitude of any frequency because at these long wavelength the source can be modeled as a point.

Of course you can estimated the energy radiated seismically by integrating first the energy at one station in the spectrum and then integrate in space considering the variations of amplitudes according to the fault plane solution, and then you need to add the energy in the P and the S-waves. After that you would have the energy radiated, but would know nothing about the energy that went into heating the fault plane by friction and the energy possibly used to break rocks, plus there is also the potential energy stored by uplift,

As I said, it's best to study a text book, perhaps Aki and Richard.