Manchuria would be a priority for Russia as it is their first and probably only door to an open ocean, there wouldn´t not be heavy ethnic problem as other part of China because there weren´t many Chinese before 1880 if I`m not wrong. Korea would probably stay with OTL border but as a vassal of Russia.
Persia probably would probably settled with Britan as OTL 1907(I´m not saying same border or same treaty just a similar version) rather than outright annexation.
Russia expansion in Anatolia would be in land with significant christian community so probably direct expansion in Armenia, puppet Greece in west coast and Assyria maybe?
Romania could stay as a puppet to have less minorities(maybe give them Bessarabia to reinforce their relations?)
Russia would definitely have Ruthenia in this TL so Galicia would be the definitely border in the in this area but puppet states in Czechia and Slovakia are likely too.
The border between in Prussia and Russia is really hard to settle, even if you go far there is still open plain and hostile minorities(polish and german) so I really don´t know where Russia would like to have a border.
Mongolia is hard to control so I don´t know if it makes sense for Russia to have direct administration rather than vassalage. The land also is not available for Russian settlers.
Kashgaria is the same situation as Mongolia but having a puppet here would help the other Turkic people in main Russia to create revolts so is better direct control here.
Afghanistan is likely to stay as OTL, even if Britain has no way to invade Russia from central Asia I think that having a buffer state is better for both, mainly for Russia that need British bless to mantain his new trade route in the east. So no Kashmir.
Scandinavia would probably stay as OTL, Finland could be integrated but I don´t think it is a necessity for Russia. Russia would definitely want to take more northern islands possible.
I don´t know how Alaska could be mantained in the long term, if Russia for some reason owns the land when the gold is discovered I guess that they would never sell the land in the hope to find more gold, but I don´t know if the British would accept that. I think that is ASB to have Russian West coast, Russia has no way to attract and settle people here without good ports and good logistics in Siberia and Kamchatka.
I can´t help you explain how Russia could reform, for starters an earlier abolishment of serfdom.