Well, it's powered by bleeding exhaust from a very big rocket.

One of my favorite clips to give a sense of scale for rockets is this one. https://www.youtube.com/watch?v=70u748VALt4

I show someone and then I tell them, that's not the rocket exhaust. That's the exhaust for the engine that runs the fuel pump for the rocket.

Nope, Raptor is full flow staged combustion, so both the fuel and oxidizer have dedicated preburners and turbopumps each.