"네, 나는 영어를 합니다."

Well, 네, 나는 영어를 말합니다 feels very awkward, but if you were to change 영어를 -> 영어로, then it can mean Yes, I am speaking in English. 영어를 해요, is correct, but this course likes to focus on more formal ways of saying Korean, or 존댓말, so the Korean sentence given as the original question is correct in this course. But 네, 나는 영어를 해요, 네, 나는 영어를 할줄 알아요, all mean the same thing, which I speak English (second example literally means I know how to do English.