Yea, I think your problem is at least in part the fact that you are trying to use water to thin ModelColor for airbrushing.  Yes it can work, but categorically speaking it is not the best.  Their thinner product is by far the foolproof choice.

To answer your other question, yes even when thinning with their thinner product, its not uncommon to see a little separation as a white streak on the surface in the cup half way through doing a coat, but simply swishing the airbrush a bit is enough to mix it back up enough to finish the coat.

PS, if you do try a few shades of ModelAir, for my part I've found they double very well for brush painting (just goes on a little finer).