Sunnyhope, this is 'free motion' quilting, if you go on utube you will find lots of examples of how to do it. You have to drop the 'feed dogs' the little teeth that push the fabric through the machine, then you can move the fabric around.
The bias binding can be hand stitched or stitched on the machine, if you have a twin needle you can stitch both sides at the same time if you match up the width :D