Dawn can etch dishes. Paint too. Buy car wash.
Polish is like sanding. If you wax and then polish, you might as well skip waxing as you are taking the wax off with polish.
Nu finish is junk.
However you do it, the paint needs to first be cleaned. Then it's waxed. Cleaners are either abrasive type or chemical type. Zymol is chemical. Both will smooth the finish...just in different ways.