Originals of the invitations are always required. The Russian consulate in Beijing issues Russian visas only for Chinese citizens and the foreigners who have an official status in China (working, studying) or residence permit. It is recommended to apply at the Russian consulate in Shanghai as they are easier to deal with and might sometimes issue a visa even if you're not a resident in China. However, it is not guaranteed that the consulate in Shanghai will cooperate, so if you want to be safe get your Russian visa before you travel to China. It might also be possible to obtain a Russian visa in Beijing through an agent.
On a side note, this is the largest embassy in the world.
Latest news from the consulate:
Russia.Org.Cn
To order Russian visa support online:
Way to Russia Visa Support
