I agree with Kristakz that you should not wash it again until you have assembled it back into a quilt. You may be able to spot treat some of the spots to see if you can find something to take them out. If they are on the white, I would go ahead and try an oxyclean paste.
If the hexi's are that small it will have a very irregular boarder and will be tough to bind. Yes very narrow would be the only way to do it. Is the outer row all white path hexi's? If so I might try a colored binding if you could find a solid close to the pink or blue in the quilt.
As far as quilting, boy that would be alot of work to go around each piece. Maybe just around each circle of color and along the path. Should be close enough for most battings today.