Good questions. It is rather facinating to me that people got their mail at all, but apparently they did.
The mail was delivered to the post office and people came and got their mail -- unless they hired a private carrier or made other arrangements. "RFD" (Rural Free Delivery -- home deliver in rural areas) does not began officially in the US until 1902.
There were very VERY few "towns" in the Indian Territory prior to the Civil War. In the Cherokee Nation, there was Tahlequah, Ft Gibson (Keetoowah), and Webbers Falls. In the Creek Nation there was North Fork Town. The Choctaw had Scullyville, Boggy Depot, and Doaksville (and maybe Perryville). The Chickasaw had Tishomingo. Other than that, there were stores, stage stands, grist mills, court houses, schools/churches, large farms/plantations -- these places are all candidates for a post office as gathering places for the rural population.
By the way, when you seen "C.N." in the heading of the correspondence, you're not seeing how the envelope or mail pouch was addressed. On the inside it might say "North Fork Town, C.N." and on the outside it might say something like "North Fork Town, Creek Nation c/o Fort Smith, Arkansas". No one made an issue over whether a person was across a boundary line (Creek Nation vs Cherokee Nation). A post office at Tulsa (Tul-Se or Tulsey) would have served anyone in the vicinity regardless of their citizenship or the location of the boundary line. A post office may have only served a dozen families or so that lived within ten miles of the place. By today's standards, it was a very informal process that worked because people cooperated and had respect for the mail.