Sometimes I think that, when poetic parts of Scripture talk about some attribute of God, the difference between 'figurative' and 'literal' is just a matter of what part of the universe you're watching from.
Does God 'sing' over us? In the passage which started the thread, my Bible says He will 'rejoice' over us. Rejoicing isn't always singing, and singing isn't always rejoicing.
I think He sings. Is it audible to human ears? No, nothing so mundane -- God is spirit, and the sound of His voice goes way beyond the physical -- but could include it if He decided that it needed to.
I think He sings. Why else would music, of all forms of communication, go the farthest to communicate on an intellectual, emotional, physical, and sometimes spiritual level, if it wasn't somehow a picture of how God communicates with us?
I think He sings. Music is structure, creativity, and energy all wrapped up together -- yet another picture of God.
I think He sings. I think He's a tenor, but then I'm a tenor, and we tenors are noted for having egos larger than the Tower of Babel ever got!
p.s. - Anybody ever read the Silmarillion by Tolkein? Interesting imagery with regard to music, as I recall.