yeah you can wash then wax, just the aim of QD or a cool wash is to keep the wax you're already got in the paint on and not to wash it off.
polish contains really fine abrasives that effectively smooth the surface to make it smooth and remove fine sratches, polish will also add a gloss but not as much as a glaze
glaze basically give your paintwork the gloss / wet look glazes don't contain any adrassivs so you apply after polishing. glazes also offer no protection so you need either a sealant or wax on top
sealants are pretty much a liquid resin that forms a protective layer over your polish / glaze
wax adds a further shine and also helps protect from uv / contaminates wax also causes the beading effect and water will sit on top and slide off, this means you wont have to worry about water marks after rain
to do a full job you would probably use a foamer to cleans the car, wash rinse and dry, clay the car (remove below surface contaminates), use a paint cleaner (on top contaminates), polish, glaze, seal and wax