The black screw on that engine just holds the carb togehter really... it CAN limit how far the carb barrel can close, but if its set correctly it will allow the barrel to fully close which shuts the engine off. (and thus that screw SHOULD not limit how low the idle can be)

The screw you have LABELED as the idle adjustment is where you adjust the idle... Hmm... should be obvious.

It is possible for hte stops built on that carb to be preventig you from adjusting for best idle... But with the adjustment centered between the stops... you should be able to make it idle better.

Most engines will refuse to have a stable low speed idle until they have been "broken in" some. give it several tanks to a couple of gallons of fuel useage before you worry too much about getting the low speed idle adjusted "perfectly." (its never perfect on a 2-stroke... you have to tweak it a bit with weather changes.)