Short answers, pulled from the story.
Official contacts between the Russian Empire and the new United States began in 1776. Russia remained formally neutral during the American Revolution which lasted from 1765 to 1783.
The Russian Navy's Baltic and Pacific fleets wintered in American ports in 1863 with one division stationed at New York and another anchored in San Francisco. This gesture supported the Union largely because it served as a counterbalance to British power.
In the Alaska Purchase of 1867, the land was sold to the United States for $7.2 million. Only a few hundred people lived there in 1867 before Russian administrators and military left Alaska.
On the 25th of December 1991, the Soviet Union dissolved after Gorbachev resigned as general secretary of the Communist party. Russia assumed the Soviet Union's UN membership and permanent seat on the Security Council along with its nuclear stockpile.
Three weeks into the Russian air campaign which began on the 30th of September 2015, Vladimir Putin met Bashar al-Assad in Moscow to discuss their joint military campaign. Bilateral negotiations over Syria were unilaterally suspended by the U.S. on the 3rd of October 2016.