For the first question:

Generally good. Since the independence of the United States, America had retained good relations with Russia, which viewed the younger nation as a counterbalance to the influence of the British Empire, with which it was often in conflict. I suggest Ronald Jensen's The Alaska Purchase and Russian-American Relations.

For the second:

There are multiple reasons, but the largest were American manifest destiny, Russia's inability to defend the boundaries of Alaska militarily and economically, and the economic effects of the Crimean War.

After the American Civil War, Secretary of State William Seward attempted to expand American borders politically through purchases. His most successful grab was that of Alaska, but he also attempted to deal with Denmark to purchase Greenland and the Danish Virgin Islands. The latter purchases failed due to the antipathy Congress had for the Johnson administration. The United States ─ at least Sec. Seward ─ was interested in purchasing it.

Russia was interested in selling it because just a decade before, the Crimean War had proved the vulnerability of Russia's extended Pacific possessions. Konstantin, brother of Tsar Alexander II, was head of the Russian Imperial Navy and firmly believed Alaska was indefensible in the event of conflict. It had avoided capture during the Crimean War only because a backdoor deal between the Russian-American Company and the British government (with the help of the Hudson's Bay Company) secured Alaska's neutrality.

While Alaska was a money-earner for the RAC, its distance from European Russia meant Russia had a loose hold on the area. The RAC had to pay for every soldier and priest in the territory, and thus it supported policies that kept Imperial government small. This left Alaska vulnerable to border-jumpers like the thousands of gold prospectors that flocked across the border during the Stikine Gold Rush of the early 1860s.

Konstantin and others in Russia felt the United States was destined to control North America, and if Russia attempted to hold onto Alaska, its possession would either be swept away by the American tide or be a spark for conflict between the two nations.

Konstantin felt that the sale of Alaska would help Russia pay off some of its Crimean War debts while avoiding those problems. Russia sought $5 million in gold, but it negotiated well and was able to get almost half again that amount from the United States.