Yeah, I hate those spam folders sometimes.
Without being able to see the screw, it is impossible for me to say where it might have come from.
A screw with a spring on it could have come from a lot of places.
Did you open the carburetor up and actually find it in the carburetor, or did you find it laying in the intake area (on taop of the carb) when you removed the air filter?
If the latter was the case, it is most likely the choke stop, and the choke is not operating properly.
This could also account for the engine speed issue.
Does it only overspeed in MANUAL, or does it also overspeed in AUTO?
When was the last time this unit had a good tune up?
When was the last time you had the gas pressure checked?