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Answer: Very fundamental question and I am afraid I do not have the answer. This is how the nature is. The nuclear force, in its range, is stronger than all other three. The strength will be determined by the basic interactions between quarks.
Answer: Yes, there is a field. However the length scales are small and so it has to be in quantum framework. Thus usual notion like force and motion of a particle will not be applicable. We do talk of a nuclear potential, which is essentially a field description.
Answer: Indeed the coupling consts are defined like that. These are dimensionless quantities created from variety of quantities related to that interaction. You are very right that why the coupling constants are so different, is still under theoretical investigation.
Answer: Yes, you can. Indeed the changes in energy and mass are related by E = mc2 equation.
Answer: Just look at the radius of the electron orbit for a hydrogen like atom. It is a0/Z. Roughly the distance of electron orbit goes as 1/Z. The volume will go as 207^3.
Answer: Thanks. I will look into it.