Vivacity suddenly doesn’t start anymore

Hello friends of the night, this is my first topic, so please be lenient with me. I have never had anything to do with motor-powered vehicles (except for the car rides during my driving licence) and bought my first scooter 3 days ago: A Peugeot New Vivacity, 49ccm, 4T with 2500km, EZ 2010. He jumped on several times without any problems and I drove from the place of purchase about 20km to me. There I then parked it and stood 3 days covered outside The previous owner gave me the tip to press the gas tap several times before starting, to “pump some gasoline ahead”. That worked once, too, the engine ran a few seconds, but when I tried again, nothing went on again. I already tried with the start-up spray, but it didn’t work either. Also a new battery didn’t do anything. The engine orgelt in front of it, partly started. The kickstarter also seems to be a bit defective, because it can sometimes be easily kicked and sometimes it completely blocks. Besides, it does not go back to its starting position by itself after kicking, but has to be moved back by hand. This was already the case before the purchase, but the start over it was possible at the time. Apart from that, the exhaust is already quite rusty. How should I proceed around the scooter Please note that I am a (learnable) Newbie in the field. If you want me to post photos of anything or do a little more detailed, please tell me. I am grateful for every piece of advice. LG BadAssTux