The only way I've dealt with the background is to cut it several inches larger and zizag the edge so it won't fray.
Needle turn is a lot different than embroidery. You need to be able to flex the fabric so you can get the tiny stitches in without them showing. With embroidery, you want the stiches to show and not blend in, so having stabilizer helps to keep them "on the top". And with the usually longer stitches with embroidery, it gets a lot easier to pull too tight and gather the fabric, so the stabilizer (or hoop) helps keep it firm enough so keep you from doing that, yet you can pull the stitching thread tighter to get a more even lay, since it is visible.
With needle turn, you have to learn not to pull the thread tight, just snug enough to hold but not create a pucker. I also like to put a knot in about every 1"-2" to help anchor so I don't accidentally start pulling the thread tighter.
If you really feel that stabilizing the back might help as you are learning, consider a wash away stabilizer. That way when you are done, there will be nothing left to stiffen it up