Hi, Andrea -
#1) accessgenealogy. com (a free-of-charge site) has the Creek Nation's Old Settlers Roll. This roster lists only the people who were still alive in 1851, as they were due a payment, so it's not a list of everyone who made the trip from the SE USA to Indian Territory. The "Old Settlers" were the people who came before the majority of the Creek Nation..these came abt 1828; the remainder came in the 1830s. Most of these early arrivals were associated with / supportive of the McIntosh faction. (This list did not include the slave population who also made the trip with their slaveholders.)
#2) Sand Springs was / is west of Tulsa, now in Osage Co. & Tulsa Co, OK, so you might be looking in the wrong area?
#3 - Adams - there were three communities/ post offices in IT and OT named Adams in the following counties: Texas, Beaver, & Bryan Counties.
**Lastly, you might not know this but the 1860 census of Arkansas included the NON-Native Americans in Indian Territory. It lists all the white people who were married to NAs, who were working / living in IT, who were intruders. etc. It also lists African-Americans and not just those who were slaves but also those who were married to whites or Native Americans, were working in IT, etc. (Many of the slaves were just listed by one name as they did not have last names at that time.) To find them: ancestry / 1860 census: put: Arkansas under "Lived In" and mark Exact / then under "Keyword" put: Creek Nation, Indian Lands. There are 614 entries.