The Fed is buying the MBS from FnF to keep interest rates low, and FnF can then take those funds and lend them out.
The Fed can hold those MBS until maturity. The Fed receives interest payments not from FnF but indirectly from the bundle of homeowners mortgages that make up that MBC. The mortgage servicer (BAC, Wells Fargo, BBT, etc.) collects the mortgage payments and pays to the Fed. FnF does not pay any interest
The Fed does not sell MBS to investors. The Fed holds the MBS on their balance sheet.
The Fed does not require FnF to pay interest to the investors. The Fed collects interest on the MBS they do own. Any excess funds they have at the end of the year they turn back to the treasury. Smae thing with the US tresuries. The Fed collects interest payments from the US gov. They in turn return excess funds back to the treasury.
I don't think I would word it that way. FnF insures MBS and owns some MBS themselves. Shareholders do assume losses on mortgages but that is what they are paid to do. FnF makes a profit when the interest payments on the MBS they hold and the G fees exceed the losses on the portfolio.
Look at the Federal Reserve just being another investor in MBS. When they create demand it drives rates lower. The Fed wants to keep rates lower to drive the homebuilding industry. The homebuilding industry is said to be the main driver of our economy. That is the main purpose only reason they are buying MBS, other than giving FnF the ability to buy MBS since not many others are willing to do.