Agreed, device and host the same time can not work. There is this silicon switch on the "motherboard", it multiplexes the host and device mode according to the detected VBUS (of the host notebook) when plugging the notebook.
But with CM1: The moment I unplugged the CM1 in device mode from my notebook (with the USB keyboard still connected), with no further change the keyboard was detected by Linux and made available again, and when I reconnect my notebook, the CM1 was recognized as a device again though because of the USB multiplexer the keyboard was gone of course.
For me there is a different behavior between the CM1 and CM3, when doing the same steps as described in my first post. And this behavior for me is crucial, because not only the USB gadget does not work, even the "normal" USB host connector is broken somehow when adding dwc2 in the config.txt ..
I wonder how people were able to launch the USB in device mode at all, maybe something on my CM3 is broken...