Bathroom fan - What power is needed?

Is also really nonsense...

I have already read that a bathroom fan should exchange the room air 6-8 times per hour.

You actually read that, although I couldn’t find a reliable primary source quickly. Two thoughts come to mind: - You certainly have to see this in connection with short-running fans (15 minutes ...), so the actual transported air volume (in m³) is not that high. - With the high volume flows resulting (in m³/h), you have to think about air inflow—not only in new buildings. Considering only the bathroom fan is not enough. Are you dealing with a new building or an existing one?

To renovate an old building, which I am completely refurbishing myself. Among other things, I also have some concerns about the untreated wood of the exposed roof truss in the bathroom.

...I had a 100 installed. This one is operated via a separate switch, because I don't want to be unable to listen to the radio when brushing my teeth early in the morning.

That was a good decision!

When we bathe, the fan is also not really needed. However, when showering – even with the handheld showerhead! I would feel like I need a 600. Everything fogs up in no time. The disadvantage of the open shower...

If you have a closed shower, then that is already significantly better (we had that before).

Possibly install the fan above the shower!!!
And for poorly smelling stool, install a toilet with extraction and recirculation (works perfectly!!!).

Hope this helps