Your question about Tribal enrollment is a complicated one sp1814. I've been fortunate enough, here in the western U.S. to do a lot of historical study with the TsiTsiTas (northern Cheyenne) of southeastern Montana. Using them as an example, (there are nearly 600 tribes throughout the U.S.) the person would have to be no less than 1/8 "blood". This would be shown to the Tribal government by way of attestations from family members as well as a ancestral chart depicting lineage.
One of the problems is that one could become a tribal member by way of marriage, meaning a person with no "blood" could become a member as well as the children of that marriage.
Additionally, using the Northern Cheyenne as an example, there are about 10,000 enrolled members, but only around 4,500 actually live on the nearly 500,000 acre reservation (or more accurately know to them as Tribal Lands). So, as you can see, active participation in the Tribal affairs is quite limited.
The TsiTsiTas were a prominent Plains Indian tribe, but always numerically small, especially compared to the Dakota-Lakota, whom we know as the Sioux. (Is that your young son? Yes, responded the man on the streets of Rapid City, South Dakota. What's his name? Young Bear Walks Upright, responded the father... Unusual name no? Well, actually not, since the mother and I are both Lakota. Oh, you don't look Siouxish...)
I'll get my coat...