I am answering only one of your questions: How come no native American states have formed?
Arguably, some states have formed.
Paraguay: According to Wikipedia, 90% of the population speaks Guaraní.
About 95% of the people are mestizo (mixed Spanish and Guaraní Indian descent. Little trace is left of the original Guaraní culture except the language, which is spoken by 90% of the population.
Bolivia (officially the Plurinational State of Bolivia):
Since Bolivia was created as a state on its own in 1825 it has been a multiethnic society. As a result, Bolivians tend to treat their nationality as a citizenship instead of an ethnicity.
In Bolivia, a 62% majority of residents over the age of 15 self-identify as belonging to an indigenous people, while another 3.7% grew up with an indigenous mother tongue yet do not self-identify as indigenous
Nunavut (part of Canada): above 80% of the population identify as Inuit, and Inuit is an official language.
Comanche Empire: Author Pekka Hamalainen argues that
In the eighteenth and early nineteenth centuries, a Native American empire rose to dominate the fiercely contested lands of the American Southwest, the southern Great Plains, and northern Mexico. This powerful empire, built by the Comanche Indians, eclipsed its various European rivals in military prowess, political prestige, economic power, commercial reach, and cultural influence. Yet, until now, the Comanche empire has gone unrecognized in American history.
Sequoyah (proposed state of USA in early 1900s, blocked by Congress, area now part of Oklahoma) is mentioned in another answer.
These states can be defined as "native American" on a demographic and/or linguistic basis. If you look at the question historically, you could probably argue that the states were set up by Europeans. However, as a lot of the available written histories were probably written by Europeans, it could be that there is an inherent bias blocking us from seeing these countries as "native American" (I will not argue for any of these points of view here).