Thanks for the answer!
I've read a fair amount about servo signals and such, but I don't quite understand it all since my knowledge of RC cars in general is pretty bad, even though I've read a fair amount about them as well.
As far as I understood, I can just replace the signal wire to the ESC and servo with the wires from the Raspberry Pi using PWM?
I've drawn a wiring scheme the shows my understanding of how to wire the car:

Would something like this work or am I way off?
Sorry if I sound stupid or ignorant, but I'm completely new to remote controlled vehicles, and I don't know much about them. But that's why I'm doing this project, to learn.
Thanks in advance!