Raw edge applique does not typically use stabilizer, but if you are going to do a machine satin stitch then yes, I would recommend a nice tear away stabilizer while you are doing the satin stitching. Personally, I don't like satin stitching, but a blanket or applique stitch will fray slightly when washed. If you are making a wall quilt, you can have it laundered at the cleaners & you should be fine. If you plan to use this as a bed quilt, a tight stitch is the way to go if you don't like that more casual frayed look.
Jinny usually gives very clear instructions in her classes. I would look to see what she recommends in the Craftsy class that accompanies the kit.
Sorry, just read that you are going to hand stitch. Fusible is slightly more difficult to stitch through than just fabric, but there are techniques to make it easier. (1) Don't fuse until you're ready to stitch. The longer fusible sits on the fabric, the harder it is to stitch through. (2) Use a lightweight fusible whenever possible. It may not have as strong a hold, but it is much easier to push a needle through. (3) Try John James Gold'n Glide Applique needles. They are coated with Teflon to move through the fabric easier. You can also try their milliner's needles, but they will bend a lot moving through fusible and you will go through a couple packs of needles on a single quilt.
Smaller stitches will prevent fraying. You should be ahead of the curve with your needle turn skills. I've seen many people put 1/4 - 3/8" spacing between their stitches when doing a raw edge blanket stitch. That's definitely going to fray quite a lot. The length should match the width, and shorter is more secure (albeit less decorative).
Maybe give it a try with a couple fabric scraps. (Also, be sure to use a pressing sheet when working with fusible so it doesn't ooze out the side of the fabrics & get on your iron.) You might find you really like this technique & remember that the quilt you fell in love with and bought a kit for was done with a raw edge technique, so it can't be all bad.
