I have used both kinds. The muslin is a one use item in my experience.
Nylon is nice, but what I have found really works well is paint strainer bags from OSH, Lowes or Homedepot.
Yes you can reuse the nylon bags. Just rinse them out is all. I stoped useing bags for hops and now just strain them out with a large strainer. Works good.
Oh God, this. I had a hell of a time scrubbing the bottom of my BK after I let my nylon grain bag get too close to the bottom while doing a partial mash. Not to mention getting all those grain husks out before I started the boil.