Sorry usually we do not use energy which is a time-domain quantity and depends on the time signal. I guess you mean the power transmission. then it is abs(S)^2.
S parameter is similar to Fresnel coefficients. if sum(abs(S))^2 is less than one the system has loss. However,associating S with the loss parameter might not be that direct, as the loss is a propagation property but S is end-to-end property. You may need to develop your own method to do this.
"2" is for intensity or power quantities.
DIfferent solvers are for different purposes and have different sources of errors.
This forum is mainly for simulation.
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