I have heard that a Moen single handle faucet can screem, but I have never heard it myself. A loose bibb washer inside just about any faucet can cause a machine gun type vibration. Also, sometimes when water is turned ON, the pressure in the pipes drops enough for a toilet ballcock to come ON for a minute…If it or its cut-off at the wall has a loose washer, you can get a screem or machine gun pipe rattle. None of these things fits your symptoms perfectly, but maybe they will get you looking in the right area. Good luck.