How to explain electrons' interaction via the weak force? What is the piece of theory which dictates that electrons interact via the weak force with other electrons and protons, and how can this force be understood in terms of what I am more familiar with i.e a coulombic interaction and dipole moments ...
 A: 
A) What is the piece of theory which dictates that electrons interact via the weak force with other electrons and protons, and how can this force be understood in terms of what I am more familiar with i.e a coulombic interaction and dipole moments ...

Electrons interact via the electromagnetic force dominantly with other electrons and protons, not the weak, because as the name indicates the weak is weaker than the electromagnetic by orders of magnitude.
Particle physics accepts and has modeled in the standard model that there exist four interactions a the elementary particle level, corresponding to the four  relatively macroscopic forces, gravitation, strong (as nuclear force observed first), electromagnetic, weak( neutron decay observed first) . 
From the standard model particle table all matter as we know it is composed: protons and neutrons made up of quarks go on to create the periodic table of elements and then solid state appears.
The interactions of protons, neutrons and electrons are what dominate macroscopically.
The gravitational force is very weak and can be ignored except in the early seconds of the Big Bang model.
Quarks can interact with all forces, strong dominant, then electromagnetic, then weak. Electrons and quarks interact with the electromagnetic and the weak.
Two elementary particles interacting do so with one dominant force at a time, depending on their quantum numbers and the hierarchy of forces on which is dominant for the specific case. 
For the formation of solids and liquids the electromagnetic interactions of electrons and nuclei are dominant. The orbitals of the electrons around the atoms and molecules have shapes ( dipole)  that allow for spill over potentials of the  positive from the nucleus and the negative from the electrons that allow bondings, positive with negative.
To clarify , in a simple excitation of an atom it is not the electron that interacts with the electromagnetic field of the photon. It is the whole atom which quantum mechanically will absorb the energy of the photon and change the orbital of the electron . The system nucleus electron is not a planetary system controlled by classical mechanics, but by the quantum mechanical state function whose square gives the probability of finding the electron in a specific locus.
