I would probably applique them onto a larger piece of fabric in a mosaic design - like tiles in a mosaic with space between each one. I hope that makes a tiny bit of sense? Sorry I can't find an example of this anywhere, but I think it would look cool with lots of "wonky" squares of different shapes and sizes.
Hmm that's so interesting...I use a low loft polyester bat exclusively and I don't have any problems with it for hand or machine quilting, and I always use cotton thread. I'm sure polyester bats can very a lot depending on the loft, the manufacturer, etc., but I've always been really happy with the one I use (June Tailor Fusible).
I saw a lecture on batting once by a very famous machine quilter, and she suggested that quilters make sample squares (like plain mini quilts) of tons of different kinds of batting to get a sense of what fibers, brands, etc. they like best and how different kinds behave. She pointed out that you might want to use different battings for different quilts depending on the effect you want. Great idea, but it would take a lot of time and energy to put into practice of course. But part of the point is that only you know what you like, so you kind of have to try different things and make your own decisions. Other people's experiences can only tell you so much.