If you have reserve, wait til you are on it, then use the main position as an off position.
If you have no reserve, you would have to find the vacuum line to the petcock and pinch it off or something like that.
Maybe someone with a spree can help.
Same on the adjusting screws on the carb, You need someone with spree experience to tell you which is which but most carbs have at most, an idle speed adjustment and an idle mixture adjustment. A lot of small engines do not have the idle mixture adjustment.
When the engine quits, is there any easy way to get to the flywheel or something similar and rotate the crank by hand to see what it feels like?