First, it is normal to set the throttle control something like one quarter open to start that kind of engine (el cheapo bent shaft whipper snipper) - they often have a throttle stop for the starting position. Second, they usually run miserably until they warm up - it isn't difficult to keep them going provided you leave them in the starting throttle position and let them scream, but it's best not to load them for a couple of minutes. Third, even after warm-up, unless you have it set to idle pretty fast, it won't idle. Fourth, it cools off very quickly: you will need the choke to restart just five minutes or so after shutting it down after a hard run.
That is the way it has always been with my Craftsman if it has a new spark plug - otherwise it is a lot worse. I don't really agree that the mixture adjustments don't make a difference, but you have to run for a while after each adjustment before conditions stabilise. Have you adjusted the idle speed? If you set it to idle sufficiently fast you should be able to get it to run with the throttle at idle, the problem is that if you drop the throttle suddenly from high speed, it stalls before conditions re-stabilise to allow it to run on the slow-running jet. (Forget that stuff about idling it at a speed that allows the centrifugal clutch to disengage, that is an opium dream.)
I think the main reason for the fairly poor running of my Craftsman is that the carburetor (Walbro WA series) is way too large for a 16 cc engine. I'm not familiar with your machine.
