US or domestic census data and related statistics are noted on this page or consult the Census Research Guide. For international coverage, specifically from China, please consult the China Resources tab, otherwise consult the International Demographics tab.
Natural language searching goes a long way in a Google Dataset Search. It may be a good point of departure.
A good strategy for determining if the Census has the statistics you are looking for is examine the questions asked. There are a couple resources for this information.
From 1790-2000, the Census collected data every 10 years. This is the Decennial Census, and from 1790 forward gave researchers a statistical picture of the United States. However, one of the drawbacks of collecting data in this way is its currency: various factors can cause a geographic area to change dramatically in a short time, and relying on official census statistics that are 3+ years old could pose a problem. Researchers, local governments and others wanted reliable statistics on a more frequent basis.
In 2005, the Census Bureau began gathering data in a new way: the American Community Survey. This survey is intended to provide the public with a current statistical average of a geographic area over 1-year, 3-year and 5-year time periods. The time periods correspond to data precision, availability by geography, and currency: