You can get a set of carb adjusters which cover most eventualities but would say the splined, D and hex are the most useful and yours looks to be splined or possibly D...I took a close look at your pic but it pixelates and I can't see it clearly enough (second Photo). The carb fitted has two adjustment screws of which are circular with a little pip in one place so the tool can only fit in one place.

I would turn this screw left until the engine changed it’s fine then I would turn it right and do the same and put the screw in the middle. Something to try; either make a tool to fit or obtain one that will allow you to turn these screws. (I had a small pair of needle-nosed pliers which I ground down further so that one point obtained a grip on the side slot on the screws. Once I removed the screws - which are needle valves - I cut a screwdriver slot along the tops of the screws so I could use a flat-blade from then on). I don’t understand why I was having to keep doing it so I thought maybe another carb would be the answer ? The idle speed may be adjusted if the needle is adjusted but it may be fixed on a low cost machine like this. Ok, sketch down the location of these screws so's you don't confuse them. Before undoing the screws, first screw them inwards until they seat, and count the number of turns it took along with the starting point of the groove - you will want to return them to these settings when you are finished. Remove them one at a time. Use something like WD40 with a straw nozzle to blast clean the carb hole - press the straw right in to seal - and wipe clean the needle itself. Replace and set to the original position.This then would run fine but after say 5 minutes it would start chugging/ big down etc and I would need to do it again. By all means buy a new carb if you think fit - it may be great, it may not but I would be inclined to clean the original up inside before doing so, and replacing the gaskets/diaphragms within.

From your description of the carb screws, it would seem you are using the 'pacman' adjusting screwdriver. What carb does it have? Does it have 2 adjacent adjustable flow screws (which may well have smooth tops to prevent tampering)? If so, is there an 'H' and 'L' on the carb body near them? If so that refers to High (running speed) and Low (idling) When you are adjusting those screws, do it a fraction (1/8th) of a turn at a time. Rev the machine up, let it return to idle.....the effect of mixture adjustment isn't always immediate. This is especially necessary with the high speed run screw - as you accellerate the engine, it should buzz and then start to slightly 'four stroke' as it reaches maximum RPM. Some people think the engine is misfiring - it isn't.When the machine is running, keep it idling as fast as possible (without engaging the clutch etc). These tiny engines have little 'flywheel' effect to keep it turning over. The first photo, sometimes but not always, there is a plastic or soft rubber tiny bung in the brass bit and if you prize this out, there will be a screw underneath which is actually the top of the barrel needle and you can richen the low speed running by undoing it a little. I have had machines like this need a slight adjustment but also had the fuel line issues as above on irregular used machines. Could you take a look at these photos of a carb and advise the possibility of adjusting mixture or is it fixed etc without adjustment.