FTTH/Network/DECT/IPTV is it correct?

Only if I want to bring the analog signal to a specific network socket do I connect the Fritzbox directly to the patch panel using the RJ11/RJ45 cable and can then connect the analog phone to the corresponding socket. Correct?

Yes. Directly patched through, without any electronics in between.

I now have to decide where the ceiling boxes for the APs should be placed. In the basement, I would put it where "Flur" is indicated. On the ground floor, I had planned two APs. One in the entrance area to also cover the garage and one in the hallway at the level of the stairs to cover the terrace. Is that too many? Would one central one in the hallway suffice? And does there even need to be one in the basement since the FritzBox is located in the technical room anyway?

Plans can be found here:

Based on our current experience, we will have two APs on the ground floor with only a slightly larger area. I would probably do the same here, but place the second one at the staircase landing (going up). Then it might still be enough for the terrace.

So, as marked here in yellow?

No, for me that is the exit (from the cellar stairs). I wrote

to the stair tread (upwards)

This meant the stairs to the upper floor, otherwise the two APs overlap too much.

More like this... and if you need Wi-Fi in the garage, I would put something of its own there. The wall to the garage should be solid.