Hello dear!
Well, Russia and Mongolia are bordering, but that part of Russia is not a really Russian region! It is Siberia and it is not densely populated, as Mongolia, also!
Through the time, the government of Russia has sent people from another places into Siberia, thus most of the people now residing there are not really local people!

Mongolians do look Asians but not all Asians came from there.

Siberian Russians look a little like them but most Russians look European.

Mongolia has it's own language but many also speak Russian since it is a part of the former USSR.

first, what you call Russia, is Russian federation, and it unites (not always by a free will !) many different nationalities and ethnic groups and religions. so it is nonsense to generalize them.
second, all Asians, as all Caucasians and the rest of the world, come from the Himalaya, and the territory around.
third, Mongolian people look like mongols…
fourth, Mongolians, and Tatars have a great past. they where famous for their warriors. and their skills in riding. they were first who had stitched clothes, such as trousers.
under their influence, Russians kings, and landlords got united, to protect them self from the Tatars and Mongolians. Russian Kingdom was born. (not the Russian federation). But that's already thousand years back.
While the communist's rule, most of the Buddhist monks (major religion) in Mongolia, and also those on Russian territory where executed. the temples destroyed… right now they are finding back to their originals, in tradition and religion.
the rest see in a history book.
and they are Asians, so they look like Asians… but very earthy… opposite to Japanese for example.

Hi dear, Mongolia is located between Russia and China (bordering only these 2 countries. But I would like to note that many Mongolians live in Russia or China. In Russia, you can find some autonomious regions or cities like Tuva, Irkutsk that there are many mongolian ethnic groups are living. Also in China u can find Inner Mongolian autonomious region that Mongolians live there. But fortunately, Mongolia is an independent country and has its long ago history, and these days Mongolians are celebrating its 800th years anniversary of Mongolian Great Empire and Mongolian these history known to out as Chinggis Khan.
About Koreans say that they come from Mongolia, as you know in the 13th century, Mongolians united half of whole world and Mongolian nationalities left in rest of the world. Many people in many countries like Turkey, Korea say that they are from Mongolia. But not all from Mongolia, u can be sure.