I happen to work for the treasury, and I can tell you the Fed is not actually part of the treasury, though they have govt. appointed chairmen. It's considered quasi gov. They charge us (the Treasury) money for their services, I have to deal with them all the time.
I can also tell you that the Fed does not directly print money, that is always done at the U.S. Bureau of Engraving and Printing. The Fed does however have control over how much money is injected into the economy.