It's ok to post all those pics. Whatever helps make your information clear.
Also, I'm glad ueleu can provide some information here, as I have no personal experience with your mixer and the UAC200. Please continue to add information ueleu.
I do have some things to say, which I hope offer clarity for your confusion.
First of all, let's get rid of that DEMO driver. I don't know how it got there, but after some googling, you're not the first to get this.
Check all of the following places, and remove it from there.
And then reboot. The right driver selection without DEMO should now show up. If that's ok now, let's continue.
Let's next understand the philosophy of what we're doing. We want to do the mixing in the actual mixer. And we want to monitor in the mixer. Get your thinking away from the computer and the programs. The mixer is where it's at!
One thing we must do is not have more than one thing playing to our sound output. We want only Radiologik DJ playing into the mixer, not nicecast. Nicecast has a volume control right under the start button. Move that volume slider all the way down. We don't want to hear a second output from nicecast. We'll monitor using headphones on the mixer.
The next thing we need to do is play audio from Radiologik DJ into the mixer. If you wish to use the UAC200 for the output, choose that in Radiologik DJ preferences. The sound preferences for the entire computer do not matter, except the volume levels you set in there for each one. I recommend maxing those out, and use the mixer to control the volume. At this point, we should have Radiologik DJ playing into the mixer, and you should be able to hear that in your headphones plugged into the mixer.
Now, the output from the mixer goes into the computer through that UAC200. You want to have nicecast source set to that, as I see you've previously done in one of your pictures.
On a completely separate computer if you can, monitor the nicecast stream to confirm you hear your music and microphone being mixed together. You could do this on your same computer, but must be sure not to listen to the wrong thing. If you set your default audio output in your mac preferences to use the Built-in Output, and then listen using itunes or some other program that can connect to your nicecast stream, you should hear it, but *it will be delayed*. This is completely normal, and not avoidable. But the audio should be in sync, meaning if you sang along to a song, it will sound right.
Does help you to understand how this should all work? If you still have questions, feel free. And if you think I've missed something important ueleu, please jump in!