Fair and Accurate Census Act This bill extends the deadline for the U.S. Census Bureau to complete the 2020 decennial census of population and related tabulations and provides $400 million to address the impacts of COVID-19 (i.e., coronavirus disease 2019) on the census and to support enhanced census activities. The bill requires the bureau to report specified information, such as (1) the total number of field staff, sorted by category; (2) the anticipated schedule of census operations; (3) total spending on media, advertisements, and partnership specialists; and (4) post-enumeration survey schedule and completion progress, including anticipated schedule for release of results from the coverage measurement survey. An institution of higher education may provide to the bureau information requested for purposes of enumeration for the 2020 decennial census of population, subject to certain public notice requirements. The institution may not provide any information to the bureau on an individual's immigration or citizenship status. The bureau may not compile, produce, or publish any data product or tabulation as part of, in combination with, or in connection with the 2020 decennial census of population or any such census data that includes topics specific to the 2020 census that were not part of a report submitted on March 28, 2017, and the 2018 End-to-End Census Test conducted in Providence County, Rhode Island. The bill provides funding for specified activities, including expanded communications and advertising targeted to low self-response communities in rural and urban areas, Alaska Native villages, and on tribal lands.