The idle speed may be adjusted if the needle is adjusted but it may be fixed on a low cost machine like this.

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.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. I have had machines like this need a slight adjustment but also had the fuel line issues as above on irregular used machines.

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 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. From your description of the carb screws, it would seem you are using the 'pacman' adjusting screwdriver. I don’t understand why I was having to keep doing it so I thought maybe another carb would be the answer ?

Specifications

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. 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. 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).