I still have such an old adapter which I used to connect to the Xbox 360 controllers, can I still use the adapter to connect and play with the Xbox One controller, or just not connect anymore?
No does not work, but if you have a micro USB cable ("normal Samsung charging cable") you can connect this with the controller.
So I wanted to get this here: https://www.amazon.de/...01L7PQBL8/ there's wireless but I can still plug in a cable?
Yes, you can even ask questions below in the product. Mostly, scrolling helps with a question already to get ahead.