US Treasury issues the debt to the capital market, so it is the investors who buy the treasuries from US Treasury.
Fed buys and sells treasury securities in the open market in order to maintain the money market balance and interest rate. It does not buy T-bills, T-bonds and T-notes from treasury directly. Open market, means a secondary market, not the initial offering.
The central part of Fed's job is the FOMC, Fed Open Market Committee. Fed chairman and all the regional fed bankers attend this committee to decide the monetory policy, ie. the target Fed fund rate. Then Fed open market operation will buy and sell the treasuries to move the interest rate to the target rate.
