GY6 keeps dying

[regdude]

Hi!
I have a Chinese 50cc scooter with a GY6 motor, I think it is called Benzhou YingYing (2006).

So I have it since 2006 and last summer some problems started to come up.
Last summer it started to die randomly. I had to wait about 10 minutes for engine to warm up in order to be able to drive it, otherwise when I gave some gas, it just lost RPMs and died. But it did that also when I was trying to warm up the engine, RPMs are too unstable. In order to drive it, I had to keep RPMs high, then I could drive it, but if it died, then I needed to wait about 2 minutes and only then I could start it up again, otherwise it simply did not start up again. I found that the carb was leaking gas by the booster (I don't know how it is called, but it's a some kind of a diaphragm that pushes extra fuel when full throttle is given), so I used silicon glue to stop it from leaking. When the summer ended, I took off the carb and took it home.

Now I tried to start it up for few days and it is almost impossible. I need to keep it starting up for about 10 minutes and then it shows some possible signs of life, but it keeps dying (still RPMs too unstable). When the engine has warmed up, then I can somehow drive it (keeping RPMs high), but that is the least problem.
The largest problem is that it keeps dying when driving. No matter how fast I drive it, but after 2-3 minutes it starts to loose speed and eventually dies, then I have to wait about a minutes and then I can try to start it up again.
And this cycle goes on forever.
I tried adjusting the air/fuel mix screw many ways, also the idle screw, but no results, those 2 screws only help to start it up for the first time.

I haven't changed the oil since 2008 and the engine oil is clear, it really needs to be changed.
What could be the problem?
I don't think is it the oil, but maybe the electric choke?