Buzzing sound from fan shroud,
I assume you mean the engine fan rather than the heater fan. My guess based on experience would be that the fan is rubbing on the shroud. Has the vehicle been in an accident involving the front end?
The bearings are failing in one of the radiator fan motors.
First step: Make sure rotating fan blade isn’t hitting anything.
Second step: Make sure fan is off and can’t turn on, put some pulling/twisting force (just a little, by hand) on fan blade, any movement noticed in the bearing?