no. a protein skimmer removes waste. if you are removing waste with water changes, then you don't need the skimmer. 20% water changes weekly isn't bad if your feeding and bio load are moderate. every tank is different. you'll have to evaluate your nutrient export and adjust with mechanical or biological methods as needed.
as far as replacing trace elements, use the same formula. if your coral load is larger, and more stony corals and your calcium and alk
are depleting more frequently, you may need to do larger water changes.