Eh, for 그렇게 I'd say do something "like that" instead. Minor difference but still different. If it were merely "do that" it should be 그것을 못 해.
What is the difference if i say I never will do that and I will never do that???
i don't think there's a difference between those two, except that the first one sounds unnatural. in the context of this sentence, the point is it's "can't" rather than "will"
I don't understand how can they still mix 반말 and 존댓말 in sentences. 저는 결코 그렇게 못 합니다 or 나는 결코 그렇게 못 해. And 그렇게 means like that, not that, G