Small update on the situation, I got it to a mechanic and he managed to "unclog" the engine (not sure what the english word would be) and it seems to be working fine. Before the mechanic the scenario was happening more and more often. Basically the engine would suddenly start to loose power, cough and then shut off. If I managed to turn it on again, it would only run for a minute max before it would start chocking again.
More about the scooter, I'm not the owner, I'm just using it over the summer. The owners have no idea when they even purchased it and the bike was not serviced ever at all. It spent almost 3 years in the garage without being turned on even once. My guess is that it's around 10 years old.
Some other issues with the bike is that it is smelling really bad. When riding it, burning oil and gasoline smell get into the hair and clothes. I have another two stroke vespa 50cc from 1999. and it's nowhere near the smell of this one.
There is also a weird grinding/knocking sound that happens randomly from the engine. It like a short sharp grind that lasts for a second and then stops. It usually happens if you accelerate a bit faster or brake a bit stronger.
My other question would be should be the first things to check on this bike and change. So far I only replaced the oil with two stroke fully synthetic. I don't have the manual of the scooter, but from what I found out online there is some oil in the engine hub that should also be replaced?
Any guidance could be helpful. Picture is here:
