Hi there ^^ I'm not Korean, but I can answer one of the questions. You wouldn't be able to find these two words in the dictionary 얼어버리다,녹여버리다 because they are composite verbs.
얼어 버리다 - 얼다 + 버리다
눅여 버리다 - 녹이다 + 버리다
In terms of the meaning, I'm not sure, so hopefully some Korean speakers would help out, but I think it means something "where are you, the one who melted me after all the time that I've been frozen", but REALLY not sure on this one. ^^
Hope that helps a little.