...I believe there is one general principle that can explain all. Something that can explain the priority of all possible reactions.
Under normal conditions sodium chloride has a crystalline structure. Each ion from $Na^+$ and so from $Cl^-$ is surrounded by six ions of the opposite charge. From this we learn that one electron from sodium is more on the chlorine side and less on the sodium side.
Since water is a good solvent due to its ionic character it is not surprising hat the aqueous solution of NaCl looks like this:
The attraction between the Na+ and Cl− ions in the solid is so strong that only highly polar solvents like water dissolve NaCl well.
When dissolved in water, the sodium chloride framework disintegrates as the Na+ and Cl− ions become surrounded by the polar water molecules...
The sodium and the chloride ions are also strongly solvated, each being surrounded by an average of 6 molecules of water.
And the one electron is still missing sodium, and chlorine with the surrounding water molecules has captured it.
There is a field in chemistry called electrochemistry. It is about the destruction and new formation of chemical bonds by electrical energy. The chemical bonds appear to be strong, but only a few volts are sufficient to destroy or re-form compounds with fluorine.
Using an electric potential difference the ions are moving to the electrodes, of course being in balance in the solution. All other of your questions depend from the material of the electrodes and their electronegativity.
The electrode could be destroyed (more true for the chlorine side) or the electrode gets plated (more true for the sodium side). All this is really a question for CSE.