Please don't insult maths while there's scientists whithin earshot. Like me.
To be fair particle physics is not my speciality, I'm more of a light-matter guy, but I still had some special relativity and subatomic physics courses
I don't know what "inner oder" means and I don't know what you mean by free Energy (the only type of free Energy I remember is a thermodynamic notion which have nothing to do here, but it's possible it's just the french jargon and the english jargon being different)
Actually, this is the opposite, the method is "calculate/measure the energy of the fundamental state of an atom, compare with what mc^2 would give if there was no defect, deduce the value of the defect".
In the current version of physics, there's a theorem called Noether's theorem that say that (among other thing) the senses "the total energy of the universe is constant" and "the laws of physics don't change over time" are equivalent. If mass was not a type of energy then
Actually, what are you calling Energy? What are these thing in this state of Energy?