Yes, you can move them left and right by pressing the comma and period keys. 8 frames at a time if you are in a 24fps sequence, 10 frames if in a 30fps sequence, when you press M or /. It's helpful to have the Avid keyboard for this. They make keyboard covers with these at KBcovers.com.
As for UP and DOWN layers...nope. I want that too. Unless I don't know about that yet and someone else does.