For China:

For "hot" spices, Sichuan pepper, pepper, Piper nigrum, which was imported and expensive, and cubeb pepper, Piper cubeba, also imported and expensive.

Other spices include star anise and a range of spices/herbs that are widely used through much of Eurasia: cumin, cinnamon, cassia, fennel, cloves, nutmeg, cardamom, coriander, basil, fenugreek, and more.

Other seasonings include: garlic, ginger, sesame seeds/paste/oil, citrus peel, sugar, rosewater (imported), dried seafood (notably scallops and prawns/shrimp), fermented bean pastes (mostly soybean, but also broad beans), soy sauce, vinegar, rice wine and wine lees, fermented tofu.

Some good sources for Chinese food history including pre-Columbian cuisine are:

E. N. Anderson, The Food of China, Yale University Press, 1988

Hsiang-ju Lin, Slippery Noodles: A Culinary History of China, Prospect Books, 2015

Thomas O. H llmann, The Land of the Five Flavors: A Cultural History of Chinese Cuisine, Columbia University Press, 2013