Before I wax a car I use dawn dish soap to wash a cleaned car. It strips the old wax off and helps the next waxing process. but make sure you wax it after.... don't drive the car after using dawn. No protection on the paint anymore till you wax it again.
Waxing black/dark cars is tricky.
The P21S is amazing on black. I sometimes do a light cut polish before using the P21S
I use a green foam pad and mist some water on the pad and have a black and decker variable speed polisher. About 1200-1400 rpm. Use various products that available to detailers.
I have done 3-4 coats of Zaino ( done many, many steps-coats )and prefer the P21S better.
Brian