Hey so far and thanks for the fast response!

Well, I guess you're just able to help, if you know what I'm talking about^^ And providing information is thebest way to get helped out.
I tried to run it in 32 bit mode, but it happened nothing, too... :/
But I solved the provlem! And I really don't know how!
Sadly I decieded to deinstall Cross and everything else belong to it like the U-Mix44 Controll Driver (CleanMyMac is fantastic for this!)...
But I don't like giving up, so I decieded to reinstall it and try it again.
The last time I connected the U-Mix44 and installed its driver directly. Than installed Cross and started failing all the time...
But for me this way still works (while writing this I'm sitting down in the kitchen every device unplugged of my Mac) and I really hope that it would be an impression for you, too.
This time I installed Cross frist. Than opend the Sound configuration and set up the Mixer Mode to 'External Mixer Cue', like it's said in U-Mix44 Manual.
After that I plugged in the Soundcard's USB to my MacBook and had a look at the Driver Settings in Cross.
"MixVibes U-Mix 44" appears and I started routing the In- and Outputs.
I had the Demo Tracks in the decks and started my turntables.
Remember, I haven't installed U-Mix44 Control Software!!
Only Cross!!
I looked down to the soundcard's output LED's and... Oh my god!
Just to be sure there's music playing in both outputs, I had a look down to my mixer and I just needed to jump, because it's working and I am happy!

I closed Cross and reopend it and it's still working!
I closed Cross, unplugged the soundcard, started Cross, replugged the soundcard and hey there, it's working!
Anyway, thanks for your reply.
Kind Regards
Dennis