"Does the Federal Reserve operate using tax dollars?
The Federal Reserve's income is derived primarily from the interest on U.S. government securities that it has acquired through open market operations. Other sources of income are the interest on foreign currency investments held by the System; fees received for services provided to depository institutions, such as check clearing, funds transfers and automated clearinghouse operations; and interest on loans to depository institutions (the rate on which is the so-called discount rate). After paying its expenses, the Federal Reserve turns the rest of its earnings over to the U.S. Treasury.
One of the things to remember is that there used to be bank clearing houses doing essentially the same thing the Fed does today. The Fed eliminated them in favor of a political entity.