Check out both of the dancing Scarecrows in Clock Town after you first attain the Song of Time- both of them teach you variants of that song that are INCREDIBLY useful.
Speaking of things you should do after first getting the Song of Time and Song of Healing, perform the Bomber's hide and seek game a second time as a hylian, full stop. The diary they give you is practically an itemized list of every character involved in a side quest. There's also a robbery near the Bomber's leader on the first night you'll get a good reward for preventing.