Anyway: Nano Router unpacked, via supplied Lankabel on Mac angrschlossen followed the enclosed installation guide, logged on to the router and simply adjusted based on the extension to show options that the signal goes in wired and is then distributed via wifi on all my devices. Additionally, the SSID and password changed and the WiFi signal "not visible" is set to. The whole procedure lasted approximately 5-10 minutes. Lankabel disconnected from the computer and router with the Nano Lankabel connected from the house connection. WiFi access on all devices - that's it!
The data rates are currently displayed on WiFiSpy with about 73Mbps, that would be enough for my purposes, however. Connected are now 1 Mac Mini, MacBook Pro 1, 1 iPhone and an iPad. All have joined without any problems and now have Internet access, as we know it ...