use batting scraps- its a great way to put to use those scraps that you cut off from a finished quilt- the flatter the better- if you use a high loft batt- they are probably not a great choice for a mug-rug
i make mine out of felted wool- so no batting
quilt them as much or as little as you want- the size of coasters- or a little larger is good. some make them post card sized
they are a great way to practice quilting on small pieces- try new stitches and experiment.
as for binding- that again is a personal choice- personally on small items i like a narrower binding- instead of 2 1/2" strips i cut mine 2" (or even 1 3/4") but wider is fine too- could even be the place to try a facing instead of binding---opportunity to try new things- and make gifts at the same time. our guild made ones in the shape of oak and maple leaves a few years ago- they are wonderful!- used very thin batting- or just a layer of muslin or lightweight stablizer....for appliqued ones i would use batting though.