Many people just grab the nearest chunk of wire to connect their project, so you have to be careful with trying to go by wire color to determine voltages.
Yes, they are a bit inefficient, you have to add the RPC load to the machine motor load to get the power used. The RPC will have an idle load somewhere around 30% of the Full Load Amps (FLA) of the idler motor.
Here is the best drawing I could find for a RPC
I couldn't find a good explanation of exactly how they work.
Yes, the 3HP RPC will start a motor at least up to 2.5 HP, maybe a bit more.
If it's in your budget, VFDs are pretty cheap. For your 1/2 HP lathe motor, you can even get one that has a 120V input and 230V, 3 Phase output. The advantages here are variable speed, and less wiring in your shop.