Hi , Thank you for your questions.
1. Confucian Temple is the symbol and carrier of Confucianism Civilization, and it is also built for monumentalizing Confucius. There are temples very famous and related to Confucianism all over China. The most famous ones are Confucius temples in shandong, Confucius temples in Beijing, Confucius temples in Nanjing, and Confucius temples in Jiading, Shanghai. Considering your trip routes, you may have the chance to visit one of the temples in Beijing. Thus I need to know about your depart time in Beijing.
2. About the Mazilu Beef Noodles and the Peking Duck, we could arrange that for you. When you're in Xining, you'll have the chance to taste Mazilu Beef Noodles with local special flavor, you do not need to go to Lanzhou for it. And in Beijing, you should not miss the famous Quanjude Roast Duck.