Lets say somehow the Russians defy the odds and manage to win the Russo-Japanese War. What terms would the Russians impose on Japan? Would they take Korea? Would it help the Czar stay in power longer? How would the loss of such a major war for them affect Japan and its military culture?
Leading up to the Russo-Japanese War, the Russians set forth a couple of proposals which probably would've shaped their policy in a peace on their terms.
Mutual engagement to respect the independence and territorial integrity of the Korean Empire.
Recognition by Russia of Japan's preponderating interests in Korea and of the right of Japan to give advice and assistance to Korea tending to improve the civil administration of the empire without infringing the stipulations of article I.
Engagement on the part of Russia not to impede the commercial and industrial undertakings of Japan in Korea, nor to oppose any measures taken for the purpose of protecting them so long as such measures do not infringe the stipulations of article I.
Recognition of the right of Japan to send for the same purpose troops to Korea, with the knowledge of Russia, but their number not to exceed that actually required, and with the engagement on the part of Japan to recall such troops as soon as their mission is accomplished.
Mutual engagement not to use any part of the territory of Korea for strategical purposes nor to undertake on the coasts of Korea any military works capable of menacing the freedom of navigation in the Straits of Korea.
Mutual engagement to consider that part of the territory of Korea lying to the north of the 39th parallel as a neutral zone into which neither of the contracting parties shall introduce troops.
Recognition by Japan of Manchuria and its littoral as in all respects outside her sphere of interest.
This agreement to supplant all previous agreements between Russia and Japan respecting Korea.
While Manchuria was firmly in Russian interests, Korea was negotiable at that point.
As for the peace, naturally, a victorious Russia would evict Japanese influence mainland NE Asia the way Japan swept Russian influence away in the Treaty of Portsmouth. Manchuria would likely be absorbed, though Korea might survive as a (nominally) independent state, for a time, as Russia hadn't entrenched itself in the peninsula just yet (only started getting mining concessions in 1898). It would, however, be solidly in the Russian sphere of influence in any case.
Indemnities are a given, seeing how costly the war was for both sides. Giving up claims on Sakhalin Island as well.
The Tsar wouldn't suffer quite as much unpopularity as OTL, nor would the socialists and communists find encouragement in a defeat of the absolutist regime, but leaving the Russian Army and Navy unreformed from their state in the Russo-Japanese War would be disastrous for any conflicts with Germany if a World War breaks out. Victory would stymie the drive for reform, unfortunately, so it's a matter of delaying the inevitable for Nicholas II.
As for Japan, Japan doesn't lose the peace, so the 1920s-30s militarism gets killed in the cradle as the military and navy can't justify their brazen acts and disregard for diplomacy (seeing diplomacy as a mere limitation to their might). After all, Japan declared war on Russia in this war. They can't take Korea or Manchuria, which reduces their empire right off the bat, reduces their industrial capabilities (no more Manchuria sending industrial resources and Korea feeding grain to the home islands' factories), and takes away their staging zones for a major war with China. A far weaker economy coupled with a healthier, more cautious approach to war (no repeat of the Russian disaster) means more better relations (or more dependence) on Europe and the USA and little to no empire building, which reshapes the Far East dramatically (Pan-Asianism might not get discredited quite so messily and Sino-Japanese-Korea relations would be strengthened by the united struggle against Western imperialism rather than destroyed by Japanese aggression and atrocities against the other two).