| The "Federal" Reserve is a *private* bank whose purpose is entirely self-serving.
It's not a private bank. Its creation and operations are detailed in U.S. Federal Code, its top management is chosen and confirmed by elected government officials, it regulates private banks with force of law, and its profits are turned over to the U.S. Treasury. It does not have the same motives and behavior as a private bank. Intentionally, the Fed is not a direct part of the political cabinet departments and is more of an independent agency, similar to NASA, CIA and EPA, and not similar to Treasury, whose chief serves at the discretion of the President and is a member of the cabinet.
The Fed does, as part of its very nature, interact heavily with private banks.
The US or Fed do not pay interest on Federal Reserve notes. The U.S. does pay interest on Treasury bills, notes and bonds.
The FDIC is an agency which is created by Congress, the same way as the Federal Reserve. The FDIC's protection of depositors is guaranteed by law, but the Federal Reserve's bailout of institutions is discretionary.