Can I also connect old controllers, such as those from the 360 or xbox one, to an xbox one s?
You can connect any Xbox One controller to any Xbox One model. So you can connect the 2013, 2015, One S, Elite 1 and 2, as well as the Xbox Series Controller to any Xbox One console, whether 2013/15, Xbox One S, or Xbox One X. You can also connect xbox One controllers, no matter which model, to the Series X | S.
The One S, Elite 2 and the Series controllers can also be connected to smartphones via Bluetooth.
Xbox 360 controllers are unfortunately not compatible with newer consoles because they use an older wireless connection, and the other way around.
A wireless adapter such as the Cronus Max Plus, which can connect any wireless controller to any USB-supported console, may help. However, it is expensive and usually starts at 70 euro.