I live in Shoshoni, Wyoming just off the Wind River Indian Reservation. Used to live on the Bureau Of Reclamation land surrounded on three sides by the "res".
Your post got me to wondering just exactly how the relationship between the reservation and other law enforcement agencies work so I called a buddy of mine who is a Divison of Criminal Investigations agent for the State. He is also sworn in as a federal officer so he can work investigations on the reservation.
According to my LEO friend, no one really understands how the system works if it does at all. For instance, his power of arrest on the reservation is limited if the perp is an enrolled tribal member. OTOH, if a non-Indian commits a crime on the reservation, local LEO will make the arrest. Now, when local LEO goes onto the reservation to assist BIA police, they do so as limited capacity federal officers for the purpose of tort liability.
If a non-indian goes on the reservation and commits a crime other than a misdemeanor under tribal law, the reservation police can not arrest the perp. In other words, BIA police can not incarcerate a non-indian in their reservation jail.
As for Indians who commit a crime, the BIA police can arrest them and put them in the reservation pokey for the little stuff. However, for a felony, the FBI makes the arrest and processes the perp through the Federal Court system. Got that?
My friend tells me he once had a federal arrest warrant for a tribal member on the reservation. Even though he is a federal officer, he had to get the FBI (not the BIA) to make the arrest. The perp then went through extradition proceedings from the res to the state just as you would from state to state.
My friend concluded our conversation by telling me that it is very confusing and complicated and not to quote him since it is clear I still don't understand how it all works in spite of his best efforts to educate me. It seems it appears not only whether the crime takes place on tribal land, it also matters if the perp is an enrolled tribal member. It also depends on whether the crime was a tribal violation (BIA police) or a federal violation (FBI).
As for federal gun laws, they all apply to residents of the reservation. State laws, such as our CCW laws don't mean squat.