Who was the first ordained rabbi to live in the USA? What was his position?
Depends on what you mean by "live in." Rabbi Rice was indeed the first one to move to the US as a permanent resident, but earlier there was Rabbi Raphael Chaim Yitzchak Karigal of Hebron, who spent some time in the (future) United States in 1773, and served during this time as the unofficial rav of Newport, RI.
In 1840 the first ordained rabbi arrived in the United States. His name was Rabbi Abraham Rice, and he assumed the position as Rov of Congregation Nidchei Yisroel of Baltimore.