적다 is writing something down — jotting, noting, filling in — narrower than the general 쓰다. The adverb says how thoroughly or how freely: 자세하게 적어서 "write it out in detail", 디테일하게 적었네 "you've written this in real detail", 자유롭게 적어주시면 "just write whatever you like". 적어 놓다 means writing it down and leaving it there, which several of these lines use. Beware the separate word 적다 meaning "be few" — spelled the same, entirely unrelated.