The Federal Reserve or Federal Reserve System is part of the U.S. Government and acts as the country's central bank. However, it operates independent of the President, the rest of the Executive...
Federal means national, as in national police force like the FBI in USA, and the RCMP in Canada, or as in a federal court or judge, not a city, regional, provincial or state court or judge.
If a witness is sworn in, it falls under the heading of perjury, definitely a federal offense. False statements in a deposition are also subject to prosecution.