I did this 15+ years ago on a model corvette. It turned out real well. I think I used acetone to thin it. Anyway, I don't know if it's just regular enamel. For one it dries a bit faster. I also seem to remember trying enamel thinner first and ending up with a goopy mess. Then again it might vary by brand.
Works really great and dries really fast (acetone used as a thinner will do that for ya) Also, to apply many coats in a short amount of time, you can use baby oil between coats.
The "varnish" component of the nail polish will rise to the surface quicker and dry even faster! Don't forget to remove the oil before each coat, of course.
As for the cleaning of the airbrush, acetone, baby oil and finishing with acetone will do the trick.