Problems with used cars – warranty available – which workshop?

Hello everyone!

A month ago, I financed a used car (Mercedes GLA 200, automatic). I picked it up from a car dealership in Berlin, 600 km away.

After a short time, I noticed the following things:

• Parking sensors react for no apparent reason.
• The vehicle occasionally reaches an engine speed of 5000 before it shifts into the next gear and cannot be shifted manually.
• On straight stretches, the speed sometimes reduces automatically, even if the accelerator pedal is still pressed. At the same time, the cockpit displays a warning that "reversing is not possible."

Now I'm wondering if I can choose any workshop I want without having any issues with coverage during the warranty period. I want to have this checked at a Mercedes workshop, which will obviously be more expensive for the dealer. Is that my right? Do you have any experience, ideally with the problems described?

Thank you in advance!