Booted into Windows and managed to find out that it is a 5100 Chipset.
According to aircrack-ng website it is supported and should work with aireplay.
Tried out to FakeAuth without wpa_supplicant, and it worked. But after that I couldn't inject again.
If I tri aireplay-ng -3 -b bssid -h XX:XX:XX:XX:XX mon0
it starts to read packages, but never send anything nor get's ARP requests, only ACKS (170 in 10minutes).