you can do without it, I used the U6 Pro on its own, but many functions are not available - you really don't have much more than WiFi - and it's almost not worth it. I got and used that first and a few months later the unifi Dream router - now I use them together in a large flat - router by the internet connection and U6 "in the other corner". I don't think it works with the Fritzbox WLAN, you then have 2 WLANs in parallel, I don't think you can use it as a repeater...

You are using the controller software. You can still use the Fritzbox as a router (not for WLAN, of course).

It needs an unfi controller. Either you use the cloud solution and pay a little per month or install the controller on a raspberry Pi or run it on the NAS in a container or get a unifi cloud key