Those are super cute.
I don't think that you will have any problem with the appliques coming loose or fraying.Your edges appear to be well covered by your decorative stitches. I have never had a problem with that on machine embroidery appliques and I have even put them on dish towels so not gentle use. I do not put any backing on the applique fabrics for machine embroidery.
If you feel concerned about that (I don't think you need to be) you could quilt an echo line 1/8 of an inch inside of your stitch down line and they will be really well anchored.
Although I know Rhinda K is correct in her instructions for the stabilizer, I would do it the way you are doing it myself. I think your quilt will turn out lovely and cuddly soft.