1). Typically the tires will either get dismounted and left at the track or carried home dismounted and occupy space in the shop.
2). I would definitely utilize a service that would dispose of them legally for a nominal $2 to $3 fee. The hard part would be making it easy to interact with the person coordinating the effort. For eample figuring out which tracks offer the service and who is the point person that you would give the tires to and pay this fee.

Thanks Carla. I appreciate your efforts in looking into an options for the racer.