Hi Melissa - serging the edges uses a special kind of sewing machine (a Serger!) that can sew over the edge & cut the fabric off at the same time, using multiple needles. I think you could just sew a stay-stitch all around the piece, close to the edge & that would help with the fraying problem. I'm not sure about the washing part though - since they were free, I guess you could throw them in the machine on gentle with cold water. That's what I would do, and, if they're going into a regular quilt, I would probably also throw 'em in the dryer on low heat. If they're cotton, why wouldn't they be washable? Then again, maybe I'm not the one to answer that, since I only separate my laundry into lights (all undies are "lights" no matter what color they are, LOL), darks, sheets & towels! But those are my best guesses.... :D
sue