Members of the tribes tried to emulate white society, including owning African American slaves. They were divided during the American Civil War as to which side of the war to support. Even within tribes, there were disagreements. The Cherokee fought a civil war within their tribe between those who supported the Union and those who supported the Confederacy.
Once the tribes had been relocated to Indian Territory, the United States government promised them that their lands would be free of white settlement. Of course, some settlers violated the agreement with impunity. In 1893, however, the government opened up the "Cherokee Strip" to white settlement by a great Land Run. And in 1907, the territories of Oklahoma and Indian Territory were merged into the new state of Oklahoma.