As I don't have a disposal, I put all those things in the garbage. :D But I do know that you're not supposed to put potato peels in the disposal. It gums it up. That's experience talking.
COMPOST! Anything that is totally organic throw in spot (away from your house) and it will break down and enrich your soil. If you ever want to garden, you need to improve the AZ soil. Chicken skin- I sometimes give it to the dog, or just throw it away.
Yeah I have heard not to put potatoe pills it does block things up. I heard orange peels are good and suppose to help make pipes smell better. As for anything else and if I had a disposal I would put it down in small amounts.
Compost!!! lets do it, come on! It would be so much fun!