What was Russian Alaska like immediately prior to the American purchase?

I've answered this question to various degrees a few different times. If you do a Google search in the format

site:reddit.com/r/AskHistorians "Alaska Purchase" "The_Alaskan"

you'll find quite a few of the posts.

Source-wise, for what you're looking for I'd recommend Lydia Black's Russians in Alaska: 1732-1867, Grinev's The Tlingit Indians in Russian America and Rabow-Edling's Married to the Empire: Three Governors' Wives in Russian America, 1829-1864.

Black's book will give you an overview of Russian America. Grinev's hones in on the Southeast Alaska experience, and Rabow-Edling talks about daily life and the struggles of culture clashes and simple existence on what was the frontier of the Russian Empire.

The later years of the Russian period of Alaska history are a fascinating time. By the 1850s, overhunting had collapsed the sea otter trade, leaving beaver and fur seal as the principal fur-harvesting resources. To keep the fur-seal population from collapsing as the otter population had, the Russians implemented some of the world's first organized conservation laws. Ryan Tucker Jones' Empire of Extinction: Russians and the North Pacific's Strange Beasts of the Sea, 1741-1867 is a nice environmental history of this process if you're interested in it.

The collapse of the otter trade starting in the 1830s had huge implications. The Russian-American Company had been granted its monopoly to regulate the lucrative fur trade with China and to better ensure that foreign traders and hunters couldn't butt in. (It wasn't successful in that end.) On the Russian end, the end of large-scale sea otter hunting meant profit margins slimmed, and the RAC began looking for alternative profit streams. It leased the mainland panhandle of Alaska to the Hudson's Bay Company. It started the Russo-Finnish Whaling Company. It created ice "farms" near Sitka and Kodiak to sell that product to the overheated populace of California.

With the RAC's focus on profit, it had an incentive to keep the Russian population of Alaska low. The RAC had to pay for the handful of soldiers deployed to New Archangel (now Sitka), it had to pay for the Orthodox priests, monks and missions spread across southern coastal Alaska, and it had to pay for its operations. The RAC operated in 20-year charters, the first starting in 1799. Starting with the second charter, Russian America was governed by naval officers who worked closely with the general manager of the RAC in the territory. The naval officers tended to be capable men, but they weren't as actively focused on profit as the RAC.

The RAC made a handful of desultory attempts at agriculture in Russian America as a means to make the territory self-sufficient, but these never really panned out because the climate didn't lend itself to farming. Only in the Kodiak archipelago and on a handful of islands farther west was there any success, and that was cattle ranching. It continues to this day, though genetic studies haven't found any surviving links to Siberian cattle.

Because of the distance from the Russian mainland and European Russia in particular, Russian America had close ties to the rest of the Pacific world. Ships carried grain from California to feed New Archangel, Kodiak and Unalaska. Boston whalers, interested in preying on the animals that lived in Alaska waters, traveled to Alaska with crews filled with Maori, Hawaiian, American and European sailors.

British and American traders sold to the Tlingit with a wink and a nod from Russian officials who also depended upon those traders (though to a decreasing degree as the 19th century wore on).

There were never a great many Russians in Russian America; at the Purchase, there were perhaps fewer than 1,000 full-blood Russians, with most in New Archangel. Kodiak was No. 2 in population, followed by Unalaska. There were trading posts and small forts throughout coastal Alaska, as far north as the Yukon River delta, but the Russians never penetrated far inland because of local resistance. One example of this was the 1851 Nulato Massacre, in which a Russian trading post was destroyed and most of its inhabitants killed. Some contemporary accounts contain lurid descriptions of post-fighting cannibalism and torture.

The Nulato situation was an exception, however. While the Russians were violent, cruel and barbaric in the early years of Russian America, these tendencies had moderated toward the later years of Russian control. The Russians had learned that Alaska Natives were perfectly capable of resistance (and in Southeast Alaska were quite well armed), and many Native groups had adapted to Russian ways of life. Intermarriage between Russian men and Native women created a large creole class that by the end of the Russian period had replaced slavery and forced work. In the early years of the RAC, Russians forced sea otter hunters to work for them; by the end of the RAC, there were large numbers of creoles who saw RAC work as an advantage and a means to get ahead. Many creoles were educated in church-sponsored schools; some traveled to Russia proper for higher education, and a handful became officers aboard RAC ships.

The situation wasn't always a calm one, but diplomats like to use the word correct sometimes when talking about relationships, and I think that applies here. Russians knew the strengths and weaknesses of the Native nations, and most of those nations knew the capability of the Russians. Black refers to at least one instance at the end of the Russian period when the Russians were brought in to mediate a dispute between Tlingit clans. Whether that is a typical example or an exceptional instance, I can't say.

It's important to note, given your time period, the effects of the Crimean War on Russian America. While the RAC used the Hudson's Bay Company as an intermediary to negotiate neutrality for Russian America, that neutrality did not extend to the RAC's ships at sea or its facilities in Russia proper. Many of the RAC's ships were captured or destroyed during the war, obliterating what had been a small but capable merchant marine for the time. Okhotsk and Petropavlovsk, the principal ports supplying Russian America, were attacked and RAC facilities destroyed or damaged.

After the war, the RAC took some time recovering, and it was only by the very end of the Russian period that it had made good its losses. In shipping, however, the RAC never really recovered before the Alaska Purchase took effect.