With regard to Indian policy, the Confederacy would probably be quite liberal toward some tribes and quite ruthless toward others.
1. The Five Civilized Tribes, and any others who agreed to go live peaceably in the Indian Territory, would be treated very well, and the Indian Territory may even be admitted as a State at some time, or granted independence as a Native American republic.
However, Indians outside the Indian Territory who continued to resist white encroachment...
2....especially troublesome tribes like the Apache or the Commanche...might well be looking at extermination. The Confederate Governor of Arizona, John Robert Baylor, advocated such a policy (he was cashiered from the army by Jefferson Davis, who opposed the policy), and he had a lot of support outside the Davis Administration. Once the war was over, a few more Indian massacres of white settlers in the southwest or west Texas may well lead a more hard-line administration to adopt Baylor's suggestion.
1. Almost certainly wouldn't happen. Most Cherokees were strongly opposed to the CSA, outside of the 10% or so making up the traitorous Watie/Boudinot faction. The OK Seminole and Creek had a very strong relationship of fictive kinship to what were technically their "slaves." All three would certainly leave rather than live under the CSA. If the US wouldn't take them, Mexico likely would. There actually was a group of Cherokee IOTL who went to Mexico, led by Sequoyah, who likely blended with the local population. Also the Seminole and Black Seminoles in Mexico, though the Seminole chose to eventually return to the US.
Probably like IOTL, OK gets admitted as a state with a largely white population that systematically stole or defrauded most of the land from Indian tribes. The proportion of Indians is almost certainly far lower, made up mostly of tribes that had been removed, ironically, from the Midwest.
2. Neither tribe had been exterminated by either the US or Mexico and there's no reason to believe the CSA would be more successful, esp with a likely policy of no large standing army, only state or territorial militias.
The most likely candidates for outright genocide would be deep within the CSA, the Seminole of Florida and the Lumbee. Both were excellent guerilla fighters, and the Seminole may get aid from Spain should the CSA make threats towards Cuba.
Some tribes that have a history of keeping below the radar would continue to do so, eg the Alabama-Coushatta, Tigua Pueblo, and the Eastern Band Cherokee.