What is the use of Neutral wax polish? Why not to buy eg tan color wax polish for my tan brogues? I mean what is the purpose for a neutral-no color?

Not sure what others have used it for but I've used it as a top coat over color polish. It can add a layer of protection over shoes that are already polished, makes the shine last longer as well. In the army for inspections/garrison duty I would shine my shoes with kiwi black to a mirror shine and then finish it off with a coat or two of neutral over it. Gave it a real deep shine like black glass. It also seemed to last longer. Other people may just use it over colored leather so as not to stain anything else.

Is this all you need to accomplish a mirror shine on the cap?

Yes you can achieve a mirror shine with this but there are more advance ways in a little practice. Please watch "the hanger project" on YouTube and Kerby will teach you all the steps from regular shine to presidential shoe shine and then mirror shine.