ow when things heat up in 1911 in Mongolia, what happens? Russia hasn't suffered a humiliating defeat in the Far East and is largely unquestioned in North Pacific. Does Russia push for a bigger Mongolia perhaps by adding Dzungaria to it? Or does Russia make a play for Mongolia and annex it outright (being more confident and wealthy in that part of the world)? Or does it go much like OTL?
I'm not very familiar with events in China duing the Revolution but my gut tells me that Russia will push for more influence due to having, or at least percieving themselves to have, a stronger military position. What exactly that entails I couldn't say.
Izvolsky (the Russian Imperial Foreign Minister 1906-1910) was pushing for an agreement with Japan regarding East Asia prior to the Russo-Japanese War, in this scenario the war never gets fought so there might end up being some sort of agreement with Japan regarding Manchuria, Korea and Sakhalin. He was also a huge proponent of the Anglo-Russian Entente... but this is only after the disastrous war.
So in a scenario where the Russo-Japanese War is avoided, three big questions occur before Mongolia is even an issue:
[*]Does Izvolsky still push for the Anglo-Russian Entente? And if so, does Britain?
I'm inclined to say that Izvolsky will still push for an agreement with Britain. The vital question on the Russian side is going to be how confident they feel in their military ability versus Germany. Without the Russo-Japanese War to highlight the issues in their military the Russians will be feeling quite a lot more confident than OTL, but the German army is still the world's premier fighting force. I don't think the lack of the knowledge provided by the RJW will overwhelm the advantages of the Anglo-Russian Entente. The Entente ties together France's two allies and creates a more united front against Germany. That's valuable for all of the participants.
I also think Britain will still go for it. Russia is a valuable ally against Germany, and that perception will be heightened with a Russia who has not had the flaws in it's military exposed by war with Japan. More importantly, Britain wants to resolve it's conflicts with Russia in Central Asia. Russia's actions in the region are vital here. Have they gone into Mongolia? Pushed more in Persia? Been more active in Tibet? Any and all of those will increase tensions with Britain. If Russia has done those things I think it will cause Britain to still pursue the agreement but demand greater concessions where it can. So a smaller neutral zone in Persia and more power over Tibet. However, that's something of a tangent to the question here and just my best guess. Suffice to say yes, I think Britain will still want an agreement with Russia.
[*]Is there an agreement concluded with Japan in the Far East?
This will depend on what Russia is willing to give. Japan felt it had a vital interest in controlling Korea and it went to war IOTL because Russia wasn't willing to settle that or the Manchurian question. Even to a Japan busy consolidating it's hold on the Philippines, Korea is still vital. If Russia is willing to acknowledge that then the countries can come to an agreement. If not then it will have to be settled somehow and we may still see a war, just later than OTL. IIRC Russian intransigence was due to Tzar Nicholas. His advisors were opposed and wanted to come to an greement with Japan. That's an opportunity there.
[*]Does the Bosnian crisis play out the same?
Possibly. Going from memory, Izvolsky worked out an agreement with the Austrian Foreign Minister that permitted Austria-Hungary to annex Bosnia in exchange for supporting Russian ambitions to the Straits. Izvolsky massively underestimated the opposition of the Russian people to the annexation and tried to make it seem like the Austrians had played him false to dodge the blame. Escalating the crisis and threatening war was part of that.