If you're looking for this switch to control the attached outlet, you would need a black wire from the brass screw on top terminal of the switch to the black screw of the outlet.
What else is on the 15 amp shared circuit? Depending on your model, it may be right at the 15 amp threshold of your breaker and any other load could cause the circuit to trip. The 120v 20 amp dedicated circuit is the way to go. If it trips that breaker than you definitely have a problem with...
When an engine surges it typically means in is running in a lean condition. If the engine has sat for a long time it is very likely that some of the jets in the carburetor are gummed up with old gas.
Since it runs well under load, that indicates the idle jet is partially blocked. I've found...