@decodancer in NF's you are allowed to bury bodily waste, so if on NF land you can just dig a big hole, dump, cover it up (not next to water sources, etc check their website for all the details). In general their rule that allows this is for 1-time use per hole as far as I'm aware, so they may frown upon dumping large amounts of bodily waste, I've never asked however. Another option is taking it into a restroom (say at a park, rest area, etc).
Gray, it depends on what's in it I'd guess. the best answer would probably be , treat it like black if you aren't sure.
As for burning trash, I imagine everyone will answer differently, I've never seen any rules about it on any NF or BLM website, tho definitely their rules around campfires would apply. I'm guessing nobody would care for paper products, but they might care for other things that would make hazardous fumes or something (plastic comes to mind). Plus some things you definitely do not want to put in a fire, like the green propane bottles or anything else that might explode. Anything with metal on it would certainly not do any good (tin food cans, soda cans, etc) in a fire.
All of this is my personal opinion along with facts as I know them from NF/BLM websites, rangers, etc. I'd suggest visiting the local ranger station/BLM field office and talking with them.
Also, this question may be better served on a different thread, where all those manly creatures can also post (unless you decidedly don't want their opinion on these questions).