You can get usually get a stubborn small engine started and running with a propane torch. Unscrew the tip (make sure you keep track of the "pill" underneath), open the valve and hold it over the air intake and turn it over. It'll run on the propane until the fuel system gets primed.
That is another one I never heard of. The first thing to get clogged is usually the float needle valve.
I guess small engines and airplanes are the last stand for carburetors. Maybe some race cars?