Yes, of course! I read a book that back in the day learning a new language was very important. People here in China learned all types of language from Korean, English to Russian. A lot of the people here were asked to major in such languages because it was important for the people to learn more languages other than just Chinese. 

That tradition I believe is still alive although some languages are more popular than others. Korean is really popular amongst Chinese people and English is also popular. I'm sure there would be people interested in learning Russian as well. Good luck!

Yes. I have met several Russian teachers. All of them were native speakers.

Try doing Google searches for "Foreign Language School" and contact the schools direct.

jinan foreign language school in my city has 2 russian teachers.

the school  teaches  korean, russian, and japanese

for europe they teach german, spanish, and french.

good luck on your search

Try Harbin , or Mudanjaing

there is a larger population of Russians business in these cities  

  because it is closer to Russia

You should pick up something there

Good luck

And see

 I even left the being in a hurry joke alone