Cool stuff on the harness working first try, I guess you had a good coach =)
Ironically, I have the same carb situation for the idle on a Chinese Quad I'm working on for a friend. New carb right from China, got it dialed in pretty good, except the idle. No air box in my situation too, the quad didn't have one when he bought it, so I just have a cone filter on it. Just guessing, but it's probably lean and needs a larger jet, but I'm wondering what yaegerb says.
Talking about that chines quad, it's a 125, but man it feels like an ATC70 for power lol. Floored on loose gravel road while turning it barely spins the tires enough to kind of slide. The ATC70 I rode was a blast, little wheelie machine, lean forward and it would spin tires, but it was gear vs whatever this china thing has, only 1 gear but shifts/feels kind of like a normal atv transmission, just the gear is super high geared since it's only 1 speed. Top speed is like 12-15mph or something like that with out reving it out too crazy.
About the stator, I wouldn't worry too much about that, unless the side cover was off or something. As long as the engine wasn't full of water, it shouldn't get damaged too easily from sitting.