Be sure to read
Working Paper 2007-052B from the St. Louis Fed's research division.
The fed mostly deals in short duration debt, which does not pay interest in the usual sense. T-bills are sold at a discount to the primary dealers (who are not the fed), and then they are resold on the secondary market. The FOMC operates to adjust liquidity and interest rates, but they don't really care about the interest they earn by doing so, only what their actions have on interest rates overall.
The Fed mostly deals in short duration gov debt except when it does not. For example, during this crisis the Fed has been buying a lot of long term government debt.
Also, I am fully aware how the primary dealer system works. Does not change anything Ive said. The Fed says they buy and sell government bonds to adjust liquidity and interest rates (which is true) but the end result is that mid and long term they always end up buying government debt as net result. Check the data of the last 20 years of the Fed and you will see how they always increase the amount of gov debt they have. Its a way of sending money to the politicians.