The mixture are EPA plugged for a reason. It is to keep untrained people from adjusting them. Echo does provide the Echo techs with a tune up procedure chart.
But as said first your make the muffler spark arrester is clean. Then you the carb for stiffen metering diaphragm and you tune per the tune up chart using a tach.
Can't even provide the stripped down chart from without the model and serial numbers of the unit you have. But I suspect you have a Zama RB rotary carb and that adjust by the primer is not a mixture screw but also a metering jet too.
Ok.....lets all calm down......I've been doing this type work for 40+ years.
I don't need a model number to tell you it would easiest just to get a kit and rebuild the carb. Just be careful when turning those adjusting screws because that also changes the amount of lubrication your engine gets. We don't want to harm it.
If you were across the street I'd do it for you. And even though it calls for a 50:1 mix. Go to 40:1 it will last a lot longer getting a bit more oil. May smoke a little more.....but I like things to last as long as possible.
Turn both screws all the way in....not too tight. Open both 1and a half turns. Clean off that plug and make sure you have fire. See if it will start.
Tell me where all of this fuel you speak of is leaking from.
Keep in mind you don't need to adjust much. Just don't screw in those adjusting screws much.....you will starve it of oil.
That other responder must have had a bad night.lol. Remember 1and a half turns out from turned in to touching bottom is a starting point.
And I'm assuming you have the carb with 2 adjusting screws.