Unifi NanoHD on concrete ceiling - which box to provide?

I'll take a look. I'm looking for the simplest solution. Just a list I can work through and then it works.... :)

Fritzbox -> patch cable -> switch -> patch cable to the various ports of the patch panel -> keystone modules -> short patch cable -> access point

You simply connect the Cloud Key to the switch.

Using the browser on any device in your network, you log into the Cloud Key and set up the Unifi devices. I can't tell you much about the setup because it was a long time ago for me and I don't have a Unifi switch. I think I watched videos by Idomix.

Is the CloudKey always connected then?

Yep, that is your controller. Once the APs are set up, you actually don't need it anymore, but it can be useful for monitoring if you want to use additional Unifi devices. If not, a Windows device with the controller software installed on it will also do, where you only start the controller when needed. Maybe also the info, in case it's not known, if you have set up an access point in the controller, you can transfer the settings to every other one and save yourself the hassle of reconfiguring. Quite practical.

I now have 2 working APs. One in the attic and one on the ground floor. They also switch between each other. That works quite well. Can I now also integrate the WLAN of the Fritzbox, which is located in the basement? It still has its own WLAN. Or do I need to use a third access point for that?

??? What do you still want with the FB then? Of course, you can also activate its WLAN, but then it cannot be managed together with the Ubiquitis, only separately.