Why is a Cessna C560 circling Washington DC during the protests?
According to the Washington Post, an unidentified C560 was also seen circling protests in Baltimore in 2015. The FBI stated the aircraft were theirs and "specifically used to assist in providing high-altitude observation of potential criminal activity to enable rapid response by police officers on the ground." 

FlightAware shows the callsign of the flight over DC tonight as JENA120, consistent with the callsigns used by FBI flights during the Baltimore flights.