2) 이렇게 and 이처럼 both mean “like this”, and they seem to be interchangeable, but I don’t know whether it’s always the case. One thing I notice is that they modify verbs, e.g., 이처럼 좋아하는 = 이렇게좋아하는 But in order to modify nouns (as in your question above), you have to use “이런”. It is still not an adjective because it means, “like such” but you can’t use 이렇게 nor 이처럼. Unfortunately, my knowledge of Korean grammar in this respect somewhat lacking. I answered based on how it appears to me.

You would rather ask your question like the following : 트와이스의 비디오를 보다가 이런 문장을 봤어요. 1) As far as the line of the song you quote, I think it's in a poetic form, something like "Shortly, (how) suddenly pouring down rain !"