1. Corner crossing: entirely depends on who you ask about this. I can tell you that I have posed this very question to members of tribal council, SRSTGF and two different tribal rangers in the field. Mixed bag of answers, but what i have settled on is that both tribal rangers I spoke with said that while someone could "make hay" over it that their complaint wouldn't go anywhere and you'd be asked not to do the same thing in the same place(find a better way in). I have never been challenged for my corner crossing there, but that certainly doesn't mean it wont happen at some point and I'm prepared to render a meaningful apology and not return to that corner again.
2. Trail cam mounting: I cant take a pic of it right now cause its at my buds house, but we made a small wooden frame out of 2x2 triangle shaped with three posts sticking up off of each of the three angles standing about 16" angled out at about 20 degrees down. The cams mount right to each of those legs with one cam facing the front of the truck and the other two facing rearward on angles....all three fields of view overlap. we just toss the frame up on the roof of the truck and voila - we can see who visits or IF anyone has. It doesn't scratch up the truck cause i just glued a small piece of harbor freight moving blanket to the bottom of it and due to its weight it doesn't move even in stiff wind (a fella does have to remember to take it off when he leaves - ask me how i remember that so well now). Works really well, i mean someone could still come up, steal the cams and do whatever their gonna do, but you will have already photographed them multiple times by the time they do this and so you will at least have a suspect(s).
3. Tribal map clarification: The YELLOW parcels on the map are open tribal lands - meaning that they are owned by and under the direct dominion of the tribes control. Your VERY expensive non-member/non-resident deer license grants you unfettered access to every inch of this land without exception. The RED parcels are also tribal lands which through one dealing or another the tribe is forced to pay state taxes on (God only knows what crappy purpose) this land is known as tribal fee land and just as the yellow parcels, your hunting licensed grants you 100% full and total access. Fee lands get hunted as much as any of the yellow, so you just have to do your due diligence in scouting your locations. There are 1 mile buffer zones around populated areas (all of the towns you will find within the reservation)- Do yourself a favor and make those 1.5 miles for the sake of not having unwanted contact with unhappy folks...I shot a buck that was 1830 yards from the boundary of a smaller town there and got an ear full along with the loss of a few hours while the whole thing was investigated and while i was exonerated in the end, I still ended up packing out late into the night due to the route I had to take and the late hour upon the conclusion of the investigation.
The Rangers I have met and been checked by over the years are some of the nicest dudes you will ever meet and they go out of their way to let you know that you are welcome there and wish you good luck and a safe adventure every time you speak with one of them. They are sticklers for violations of code (and I support that effort) and they do their jobs right, so make sure you dot every i and cross every t - as we should always be in the first place. The res has its up sides and down just like any other place. It is unfortunate that the herd is in rough shape this year (has been for a couple of years) - with a little luck, the reduction in tags will lead to a rebound (and some mild winters would help quite a bit).
Good luck out there! Feel free to PM me if you want to chat more about strategy/locations - unlike many, I'm not afraid to share what I know.