thanks for the quick reply!
I have tried to set up a static IP too, but as said, I am not able to save a profile if ethernet is not connected. So, I can fill out all the fields, but I cannot save them and get out of that screen. The button to save just does nothing and you don't go back to the networks screen.
And, yes, I get an IP both on ETH0 and on the WLAN0 (different IP's of course).
I can save a WiFi profile with ethernet connected indeed.
When I shutdown, remove the eth-cable and restart I have found the following:
1) I cannot connect when connecting to my router's wifi (living room)
2) I can connect when I move upstairs and connect to my repeater.
So, what can be different between both? I only see a difference in signal level, being around 33% in living room and 70% at repeater.
Hope this get's me closer

pietpara