while it is okay to use dish soap once in a while, i don't think it is necessary since you are going to be claying and polishing the car, which should remove any old wax.
the only way you can tell that you clayed certain areas is if the surface has a lot of containminents on it. other than that, i think the only way you can tell is when you do the baggie test, which is putting your hand inside of a zip-loc bag and gently running your hand over the surface. it should feel like smooth. if anything, clay at least the horizontal surfaces.
you shouldn't have any clay on the surface after claying. but some people do wash their car afterwards. you could also clay while washing the car using the car soap as a lubricant, but i think you need to be sure there is enough car soap on the surface.
the clay may not remove the water spots. you might want to polish them out, or try using a water/vinegar mix.
after claying, polish, then
NXT. you could top it with S100, but that all depends on whether you think it looks better with it or not. personally i think
NXT by itself on black looks great. but that's up to you. maybe do a small section and see what it looks like. oh, if possible, do two coats of
NXT, preferbly 12 hours between each coat, if not, then at least 1 hour.