Do you know if it is possible to get from Mongolia to Urumqi directly, or I have to go via Beijing?
Recent information doesnot suggest that this has changed. People keep talking about trying this route but no one reports back which suggests that no one has success.
And as well, is it easy to get chinese visa in Mongolia?
It should be possible to get a Chinese visa in Ulan Bator but I don't know the current requirements.
Maybe we will be able to get Chinese or Russian visa in Delhi. What do you suggest as most sensible option?
I wouldn't recommend trying to get a Chinese or Russian visa in Delhi. I don't have my notes but I don't recall either being easily obtained in either of these places. Pakistan might be a possibility for the Chinese visa. The Russian visa generally speaking is only possible easily in Hong Kong. I don't recall any other location in Asia where it can be obtained easily unless you have a residency permit.
Other option would be to get to Kazakhstan from Mongolia through Russia, but again I am not sure about getting Russian visa in Mongolia, even transit one.
Russian transit visas require that you have tickets for travel from the point of entry to the point of exit. Since there is no single train that travels from Mongolia through Russia to Kazakhstan, I think it might be difficult to obtain the train tickets for this route. Not impossible but difficult. OTOH I recall that some passport holders have been able to obtain Russian tourist visas in Ulan Bator, the capitol of Mongolia on occasion using UB based travel agency. Again since I am not at my computer, I can't offer the appropriate link but you might try searching this forum for Russian visa Ulan Bator.
If you travel from India to Pakistan to China to Kazakhstan, it is probably possible to get a Russian visa there but it will likely be very expensive as in the past only original documents were accepted at the embassy or consulate. These are costly to obtain and will take time to be sent from Russia.
If money is a concern, I suspect that it will be cheapest to avoid Russia and to recross China.
Ruth