I have been going through rough times at different intervals in my life, when things start to look hopeful, I often wake myself up from deep sleep singing songs. What is weird, is I normally do not know the lyrics to the song, but when I wake up, I know them all, and I run to the internet to look up the song to get more information. Is this normal?

Maybe it's that it's such a relief that you're so happy now that the sleeping you just cannot contain it C:
Singing is a good form of therapy, and our bodies are very clever.