Karla....first of all I didn't do the appliques shown. They are pictures from websites that I found showing the difference in the stitch. I did edit my post to include the links and if you check them out it gives you some good instructions on doing each stitch.
I don't know about the stabilizer question as I've only done one small applique piece in my whole life.
Babeegirl did a tutorial on using dryer sheets for applique...maybe she could tell you if you could use that method for the cats.
http://www.quiltingboard.com/posts/list/12414.page