So after another day I figured out some things:
Apple App is worse than I tought. It takes 3 to 10 attempts to even connect to the wlan of luna on the iPhone5. When finally connected I could only do about 2 up to 5 shoots, then Luna wouldn't react to the app anymore.

Android: Way better than I thought. It actually works, even with preview. Trick is to turn off mobile data while being connected to the Luna WLAN. Sure it's a bug, but can actually use the Luna now.
Turning on mobile data again while connected, I still see the live picture, but cannot shoot anymore.
Also I didn't figure out yet how to view pictures and videos on Android.