Pete, you have had the magneto coil mounted too close to the flywheel: it has scored the flywheel considerably. Use a visiting card and the slack in the coil's mounting holes to correct this. It won't fix your problem, but having the correct gap is part of the design parameters of the magneto.
The button with the long vertical travel goes into the center of the carburetor float bowl. There are two things it could do: it could push the float down, to flood the carburetor and enrich the mixture for cold starting, or it could push a needle into a fuel exit port to shut the fuel off completely, to stop the engine. So, is the button a priming device or an engine stop control? If it is a cold start aid, how do you stop the engine? If it is an engine stop control, how do you prime the engine?
