"e: wow that was actually simpler than i had it setup in my mind, stupid question, where does the cold come from?"

I'm assuming you're asking about the cold that you get out of the ac unit?

That's from the liquid refrigerant going through the expansion value , going from a liquid phase into a gas phase
The environment heats the refrigerant -> the liquid refrigerant turns into gas phase
The environment lost heat energy to the refrigerant. temperature drop from energy loss

I don't think going through the expansion valve converts it from a liquid to a gas. Going to the expansion valve should decrease the pressure so that when it easier to convert back to a gas.

Hot air is blown over evaporator coils, causing liquid refrigerant to absorb heat from the air and turn into a gas. Cool air then leaves the evaporator. The gas then goes through the compressor, increasing it's pressure, and making it easier to convert back to a liquid. The gas goes through the condenser, air is blown over the condenser and absorbs the heat. The hot air leaves the condenser. The liquid refrigerant then goes through the expansion valve, decreasing the pressure, and making it easier to convert back to a gas in the evaporator.

Yes, that is corect. I left out the evaporator's duty and combined it with just the valve
in reality, that valve is more of a flow control