Never used the mixer, but looking at the specs on the website, the Mono 1/2 Stereo button toggles between VU meters showing individual left/right levels, or an overall stereo level. It doesn’t say anything about it affecting what’s actually coming out of the speakers.. unless of course you can tell me differently 🙂 so the VU would show you either a combined stereo input (left VU for input 1, right VU for input 2), or show you whats coming out of left/right on both inputs (so left VU would show you left output of inputs 1 & 2, right VU would show right outputs of 1 & 2). I guess a practical application would be to quickly check that your levels are equally balanced, or biased to one side.
Contour – when you move the fader, how loud / quiet it makes the audio in relation to the fader position (or how quickly it pans left / right) would depend on this setting. So as you move the fader down, the level would either decrease in a nice smooth fashion (slow fade), or would very quickly go quiet (fast cut). It’s easier to understand visually, check out the Rane Empath data sheet under ‘Fader Response’ here http://www.rane.com/pdf/empadat.pdf
Applications, depends on mixing style really. I believe scratch mixers prefer the fast cut style, especially on a crossfader.