Pegasus Sky 50 Problem Cold start and sporadic power breakdown

I bought a TGB Pegasus Sky a few weeks ago. The scooter is from the year 2000 and had original 340 km on the watch It looks like new, and so far it has been doing so. Now at about 600 km it starts to get massive problems. It starts very badly in the cold start at once. You have to org some times or step into the kick starter until it runs. Before that was never a problem. Sometimes it helps if I hold the intake tube on the air filter box at the St. As soon as the engine is running, you can always start it without any problems. But after a few hours of rest, the problem is present again. Furthermore, gasoline drips out of the air filter box again and again, besunders when the tank is full. And as if all this is not bad enough he has again and again power losses where he suddenly takes the gas very badly and partly also runs out because he probably gets too little fuel. ie. That was not so until recently. Before the start of the season the oblique was cleaned and adjusted, as well as completely fresh 2 measure oil filled, and new oil at the vario. As said the scooter ran 1A until recently. What I wonder is that the scooter does not run out if I press the suction nozzle on the air filter box with the finger. Normally it would have to go out there. Does a clue in which direction to look now? Petrol pump possibly defective? Or the Joke? Or d reassembly decontamination cleaning and reassembly a new nozzle ?