Q: Do I cut away the background fabric from behind the applique before quilting?
Nancy tested this years ago on a Hawaiian baby quilt. She discovered that when she put the quilt in a hoop to start the quilting, the top stretched and distorted. "The applique thread and my stitches were all that held the quilt top together. It was a miserable experience, and I was very unhappy with the finished quilt. I have never been tempted to cut away the background fabric after that experience."
The background fabric provides a complete web that is a very strong support for your applique. As soon as you begin to cut it away you weaken the whole structure of your quilt.