I save some leftover battings to add onto batting that isn't long enough or wide enough. That way I don't have to open a new bag to cut some of that to use.
I smooth my backing out smooth and clamp it to my glass topped dining table, then the batting, then the top. It never distorts anything. I also find if I fold the backing carefully when I take it from the dryer, I don't have to iron it. Do what ever works for you. You'll be able to tell if everything is distorted, that you don't want, anything else is okay.