I'm not sure about problem #3 or #2 but as for 1 a buzzing noise from a display is new to me as for why it goes black do you have an ext monitor to test it with?  If you do plug that in and hit the FN combo key required to switch it to either both screens or just the ext monitor and close the LCD as you normally would if the ext monitor becomes black as well you are looking at a video card problem perhaps the cable from the LCD to the motherboard may be loose that could be the reason for the noise perhaps if this is under warranty I would call Dell.