(1) You can make handling a quilt this size easier by suspending the quilt. Leah Day does this. Also check the QB for quilters who have purchased the Jenoop system:
http://www.jennoop.com/suspenders.html or made their own from PVC.
(2) The cotton and wool battings would want to grab each other; however, I would still use a very light layer of basting spray between them.
(3) Shrinkage should not be a problem as long as your quilting lines are at least moderately close together -- I would estimate no more than 3" or so apart. The quilting stitches "bond" the two layers together within the small confine between quilting lines. Any differences in shrinkage within such a small area would be unnoticeable.