Power supply from the provider to the house - how does it work?

Are you talking about direct current or alternating current?

Are you talking about the technical direction of flow or the physical direction of flow?

Power consumption is, in my opinion, misleading, as it is not electron consumption in the sense of water consumption, but rather power usage. (Measured, coincidentally, in kWh)

Electrons are moving. The voltage is a measure of the electric field through which the electrons set themselves in motion. No electrons are consumed in the process; the electrons only release energy. Crucial for a cable is how many electrons move through it per unit of time. If there are too many, they already release too much energy in the cable, causing it to overheat. An analogy is the "Wassermodell für Stromkreise"; perhaps you should google it.