Can I just add a wireless controller with no receiver to my Xbox Controller and wireless receiver? And is the old receiver?

Also compatible with the new controller?

Yes, up to 4 controllers should be possible.

Also old controller with new?

Believe 360 and one use different signals so if you have the receiver for the 360 I do not work

The 360 Receiver only works with 360 controllers. There's an extra receiver for the One Controller. But of course you can also NEN One controller of the 2nd Gen. Get with Bluetooth and for 6 euro NEN Bluetooth dongle. That's how I have it at home.

With the Xbox One controllers, the receiver for the 360 Pad is not Compatible

There you need

https://www.amazon.de/...074QMN4YW/

Alternatively a Bluetooth stick (the latter does not work with all One controllers)