Will I be able to live on a RMB 2000 monthly salary? How much do I need to spend in China?

Yes, indeed you are higher paid than many local workers and teachers in China. Normal wages in Beijing and Shanghai (the richest cities) are between RMB 1500-2000, and less in rural/inner China. Since you do not have to pay for accommodation, your main expenses will be on food (some schools also provide free meals to teachers), transportation, and entertainment. Food is generally cheap in China. Single dish meals at the cafeteria on campus cost as little as RMB 4 (USD 0.50). Chinese restaurants on campus in the school area offer meals for RMB 10-20 (USD 1.25-3) per person per day. Western restaurants cost between RMB 50-100 (USD 6-12) per person per meal. Transportation options include public buses (which cost about RMB 1 per ride) and subway (RMB 2-3 per ride), and taxi costs about RMB 10 (USD 1.25) for short distances. Internet Cafe is very cheap for about RMB 4-6 (USD 0.5-0.75) an hour. Entertainment in general is also inexpensive.