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It's slowly making sense. So, if I consider the masses + spring system, the kinetic energy (and also the potential energy) should be consider as "internal energy" and not kinetic or potential. I need to digest this a little bit...
Okay, then you get a total work of zero. However, the kinetic energy has increased, and therefore some forces must be doing work because $\Delta K = W_\mathrm{all}$. On the other hand, energy is not conserved because of the behaviour of elastic forces; it is conserved because the only non-conservative force (the normal force) does no work because the change in mechanical energy $E$ depends on the work of non-conservative forces.
But if one considers the masses + spring system, the kinetic energy has increased. Then, because $\Delta K = W_\mathrm{all}$, there must be forces that do work and therefore the total work done can not be zero.
I agree with what you state, but it still doesn't clear question 3. In the masses plus spring system, I should compute the work done by all forces (the four elastic forces that are internal to this system). When doing this, the work exerted by the four forces is zero. This, however, is not correct since there is a work done by the elastic forces. What fails, then, in this reasoning?
