Where do the rings on the upper half of the planet come from and why do they seem offset from the other rings?
Let's see if I can clearly put this into words: Those are the rings passing in front of the dark side of the planet. They're translucent. The light reflected from the sun-illuminated part of the rings to either is reflecting off the cloud-tops on the night side of the planet, through the rings, to the camera.
Every nonzero finite dimensional inner product space has an orthonormal basis. It makes sense, when you don't think about it.