Small Engine Troubleshooting Problems? Ask a Mechanic Now.
First, it sounds like the choke is not being pushed fully for the cold start. The throttle has to be adjusted, so the choke link is pushed to it's fully closed position when lever is moved to the choke position. To adjust, you have to unclamp the throttle cables outer housing at the carburetor end, and slid cable housing away from the carburetor. Work the throttle and watch the linkage flip up and move the choke link.
As for engine stalling after 20 minutes, check the fuel tank cap, it has to vent the tank, or a vacuum will build up , and no fuel will get to the carburetor.
OK, do you have the engine with the pulse fule pump, or is it gravity flow from the tank to the carb? Do you have a good flow of fuel to the carburetor inlet?
Did you get the choke link where it moves to the full choke position, and if you feel it with finger, it has no slack? Moving the cable housing should not affect throttle!
See utube video above, go to 8 minute mark. to see the choke and linkage .
I see question is still open, did you find problem?