If you have a current carrying wire, and the electron is going the same speed as the electrons in the wire, then in that frame it will appear that the protons are going the other way so it will see a B field. But also you need to factor in length contraction, You need to use Einsteins velocity addition rule for the relative speeds of the moving particles in the wire. Because of length contraction we will see a different line charge in the wire and a net E field. And the one where you remove everything except 2 electrons moving side by side. Yes there will be a force cause by the E field of each of the electrons. You bring up good points.
Relativistic electrodynamics is fun.
You dont need to worry about the neutrons they have no charge and no B field classically speaking.