The stablizer goes on the back of your background piece and will be torn away after you are finished stitching. I have used waxed paper, sometimes I use coffee filters.
Fusing is done to secure the piece you are appliqueing to the background and is usually not removed. It depends on what you are stitching as to what order you fuse your appliques to the background. Sometimes I have fused several pieces together to make one applique piece using an applique sheet. It all depends on what you are making.
I have never used the satin stitch to quilt with so I can't advise you on that.