Can I apply for a China visa from Kazakstan? do I need visa to China with Georgian passport?

Yes, you need a visa to China. and the visa can be done through Chinese embassy in Kazakstan. The required documents are as follows:
1. original passport for travel;
2. Application form for China visa application (for you, both V2011A and V2011B)
3. One passport-sized colored photo;
4. If for tourism, invitation letter from China a travel agency is needed (if you visit with a tour);
5. if travel individually, you need to provide round-trip tickets and hotel bookings.
6. If you have relatives in China, you need to provide certificate for relationship.