I have backed a quilt with cotton broadcloth. It worked just fine.
I haven't used cotton batting yet as I am not yet a fan of the old fashioned crinkled look. I'm sure that will change with time. I use any number of medium weight polys for quilts. I do want to try a cotton blend to see if my free motion quilting will go better. I haven't mastered that skill. For placemats and table runners, I use a Pellon product sold by the yard. It's flatter and denser than the batts I use for quilts. It comes both fusible and non fusible. I prefer the non.
My label is hand written with heat set permanet marker (fine line) on muslin and blanket stitched by hand on the back of the quilt.