From memory I think a return flight to Beijing is about NT$17,000 which is rather expensive considering the distance. Because of the political problems between China and Taiwan, there are no direct transport links. Rather than flying straight to Beijing, you need to stop in Hong Kong, Macau, or elsewhere.
If direct flights were allowed, Taipei residents could fly to Shanghai or Beijing for a long weekend. Oh well, one day. At the moment, relatively few foreigners in Taiwan travel to China. South East Asian destinations like Thailand are the most popular.
Regarding your second question, travel agencies offer the cheapest fares (cheaper than the airlines offer).