Yes. Former enemies are now just two countries in gthe global community. Work-permits or study abroad opportunities abound. More crucial is whether there is willingness for Americans to move.
Yes,an American can emigrate to Russia after completing the essential documentation. Before emigration you have to surrender your ID documents. Again you have to get OK certificate from Russia.
It is possible, but very difficult. You would have to complete extensive paperwork, pass a physical, and have no criminal history. The process takes a very long time.