Nancy, maybe the cat/dog hairs can only be counted as embellishment if they are actually sewn into the quilt - but hey I am not the quilt police what would I know.
I think of my cat as a 'quilt-seeking device'! If I don't close the door to my sewing room next time I go in she will be tucked up comfortably in my newest creation. My dog, on the other hand, is not so interested in that room because there is no food there....most of the time
As for which batting to use....for such a long time here in Ireland the choice was polyester wadding or polyester wadding! Now we have 100% cotton batting too. I have even heard it said that there might be some wool batting to be got somewhere but I haven't tried it yet. I know that cotton batting is very hard on the hands for hand quilting because I used it all the time because I don't like synthetic substances much... but I am changing my mind now.