Your patting package should tell you how close the quilting lines need to be. If your quilting is not close enough (and that means in all directions), the batting can bunch up or even separate and you can have a mess. You will have much better luck puddling your quilt, rather than rolling it, but it can be done on a home machine, even with a large quilt. You might find that straight or slightly curved line quilting with the walking foot is easier than free motion.
I've never washed batting. Most quilters don't. If your batting is all poly, it won't shrink. If there's a cotton content, it will shrink some, and there will be some change in the quilt's appearance, but most quilters like the crinkly look.
Good luck!