Timing belt torn by oil pump

Hi, I had a stressful experience yesterday with my Vespa LX 50 with air-cooled Hi-Per 2. I drive around with my buddy in Munich. Suddenly the scooter no longer picks up gas until it finally stops and goes out. Opened directly to the parking lot of ATU and Variokasten. What do I see there? A small timing belt is torn apart in the Variokasten. The timing belt from the oil pump! The scooter, after it went out, could be started completely normal again. I But I didn’t go any further, for fear of breaking something. Now we stand there, about 7km away from home..but then the good idea of the buddy, that we just get a small bottle of 2T oil and dump it in the tank, ratio about 1:30. Bissal the scooter wobbled and we drove back home. On the way I didn’t notice anything. The scooter drove as usual. But what is very surprising is that the scooter was in the inspection before 2000km (I still had a guarantee). The belt between the crankshaft and the oil pump runs directly behind the drum (is that so?) with the weights. I wonder why it was not replaced, especially since this is already important and belongs to the maintenance. Well, the belt has to be replaced. Can I actually do it myself? Because the installation is not a problem, but you have to tighten the belt? Well, what worries me is whether my cylinder got what from the action. So I can rule out clamps or feeders, but what about Riefen? How is it noticeable that the cylinder has Riefen? Do you feel this as a power loss? What else I noticed is that my fan wheel somehow melted from the Vario nut. How can such a thing come about… did something like grind on the V-deck, because the dirt in the Vario lid was also gone at the place. P.S.: the scooter has now over 11000km down. Thanks already in advance for r your help smile I hope you can help me Dennis