I've got a compost pile in the backyard. I dump the mash tun there as I'm cleaning up. I found that if I left it in one hot pile it really started to smell bad within a day or two. If I stir it all into the pile of compost, there's never been an issue. I do try to be careful and considerate of my neighbor cause my pile is within 15' of their pool, so if they are out, I wait to dump and stir until they've gone in for the evening.
As for recycling the water used for chilling, I've seen a setup online somewhere that continually recirculates the chilling water via a pump in a bucket with ice. I've also seen it done with a two stage where the pump is in a bucket of water, strung to an immersion chiller in a bucket of ice water, strung to the chiller being used in the beer. I also seem to remember a few posts on here about recycling chilling water, I'll dig around a bit and see if I can find any links.