Manufacturer warranty for sale and tips

Hello motor friends, I am just slightly overwhelmed, is my first car sale. I would like to sell my VW UP. I am already second owner. The vehicle comes from a 2-year private leasing. The previous owner had chosen a “connection guarantee, duration 3 years following the manufacturer’s warranty, maximum total running power 100 000 km”. The VW dealer has transferred this warranty to me, i.e. the car has still until 2021 connection guarantee. If I now priv the car at sell, the connection guarantee is forfeited by the dealer or? If I would write in to the purchase contract “Connection guarantee until 2021” I give the guarantee as a private person, i.e. in case of a problem the buyer will come to me?? And another question: Am I on the safe side with the purchase contracts of Autoscout or Mobile, or do I still have to pay attention to something. I don’t want the buyer to come to me with a gear damage and then I have to pay it s. And how do you do this most usefully with the registration of the vehicle. The interested one certainly wants to make a test drive. That means I first have the car registered. If he then buys it directly and takes it with me I can not immediately unsubscribe!? Does he then have to drive away with my license plates? Thank you for your help.