"[Xi'an Famous Foods]' signature dish - liang pi, a dish of cold noodles in a sauce that hits every possible flavor category."

Xian has a famous dish of cold noodles also: 
Spicy Cumin Lamb Burger

"Snacks", meaning a wide variety of cheap foods, including various types of dumplings and bing related things (my favourite), soups, a small bowl of broad noodles with a bunch of vegetables, etc.

Not as famous as the snacks, the BBQ of the Muslim quarter is among the best to be had in China.

羊肉泡馍（yang rou pao mo - Some kind of soup with meat and what seems to be soft bread bits)，肉夹馍 (rou jia mo - Pork cooked in some sauce, cut in small pieces, then stuffed in a small bread, it's amazing)，涮牛肚 (shuan niu du - Beef stomach skewer, despite the name and appearance, it's absolutely delicious - and I'm very picky). You should also try the small soft skewers, they're the best skewers in all China!