I too am a noob but I had one of these when I was kid and I'm planning to do something similar from the ground up.
The cox engines can be found on auction sites but they are kind of messy. The battery and motor technology today is worlds better than it was 40 years ago so electric makes sense now.
As a newbie I can answer some of your questions:
- The prop should be a pusher prop and 6" is what most people choose. If you use a pulling prop you have to mount the motor pointing forward.
- A basic servo is all you need.
- The push rod is pretty basic. You can buy one or make one. Mine from years ago, was a bike shifter cable and it worked fine.
- Still learning about ESCs and motors. If your motor is brushless or brushed the ESC has to match. If your kid's RC truck is available to use, you could probably use all of its electronics including the motor and servo.