I've done several quilts with Minky backing. Some had batting, and some not. I have done regular binding, but I prefer to bring the Minky around to the top and self-bind.
For quilting, I have done both FMQ and straight stitching. I have used both a walking foot and plain foot, and have done straight and zig zag stitching.
No problems with any of it, although the Minky does get channel marks from my sewing machines advancing the fabric. They brush out however.
You do need to use a good quality thread- I used Isocord when two other brands broke.