Chengar Qordath said:
Well, although the fact that the Manchus were indeed not Chinese is a good point, I'd say the difference between a Manchu dynasty and a Russian one is very substantial. A Russian dynasty would likely face domestic problems far far worse than any the Manchu faced. I guess if you want an analogy, it would be like the difference between the Hundred Years War trying to install a Turkish king in France, as opposed to an English one.
I suppose a more Eastern-focused Russia would likely be devoting much more attention to expanding their power base in Siberia before they got around to having any conflicts with China. Conflict with China is likely a more long-term event, while in the shorter term they would focus on firming up their control over Siberia and perhaps also seeking to develop it more. Maybe they even try to attract settlers from other nations to Siberia, using the promise of cheap farming land much as the US did in OTL.
You underestimated the problems the Manchus faced. Just trying to get the Han to wear queues resulted in large scale rebellions which saw hundreds of thousands dead. Sichuan province was almost depopulated, and that's a mountainous area the size of France and Germany combined. The Russians may look a bit different, but then again they were not traditional vassals of China, neither were they a hated 'barbarian' race (the Manchus are descended from the Jurchens, who dominated North China during the later Song dynasty).
Religion might be a stumbling point, but not for the Chinese - they were traditionally rather areligious, and as long as we don't do something boneheaded like forbidding ancestor worship and desecrate all the tombs, they'd probably start cheerfully going to church. It's just another temple to them. And if Russia, like the Manchus, use the already extent scholar and gentry class (which all protests to the contrary acquiesced rather quickly to Manchu rule by and large), it is by no means impossible.
Russians are no strangers in adapting to local practises, either. After all, Moscovy was built upon the ruins of the Khanates, and we all know about Ivan the Terrible.
As to possible powerbase Western Siberia centred around Omsk and Novosibirsk might be a good place. Enough resources to power a medium-sized industrial revolution (and did, in our world), access to valuable furs, central location for trade and keeping the pressure up on the Central Asian khanates, close enough to the Volga and the plains beyond so that settlement is at least plausible, and so on, with an option to expend toward Baykal later on.