Faint to loud humming noise while driving and turning...

This sounds like the Recirculation Door Actuator is stripped. It makes a tap, tap, tap noise.

Sounds (pun intended) like a problem with the differential (that globe that connects to the drive-shaft and to the two rear tires. Maybe, one wheel has bad bearings, adding resistance into the differential.

Sounds like the low amount of oil caused serious engine damage. It won't be a cheap fix.

This noise is caused by a defective power steering pump, the vanes inside the pump are damaged, it will need to be replaced.

Without more information it is hard to tell. Is the humming noise variable depending on the speed that you are driving or constant? Could be ground, radio, pulley, compressor noises hard tell.

When does the noise occur, while driving only, or driving and idle, in gear, or in neutral and park? If it occurs all the time (while driving and at a stand still in cold weather) it could be the fuel pump. If it occurs only while driving, it may be a wheel bearing. Describe the noise (humming, grinding, whirring, etc), and what is the mileage on the Pilot? Answer my questions so I can fine tune my answer. Thanks!

the fuel pump is in the gas tank. If you hear a faint hum from the tank when you turn the key on then it is working

Normally if you turn radio and everything off that may make a noise, and cycle your key just to the on position, (not start) you will normally hear a faint "Hum" for a second or 2 from rear seat area.

The fan is rubbing ,was any of you srews striped, if they are replace with some larger screws and that will realiagn the motor

one or more of the pulley's is defective, most likely the tensioner pulley, but check them all for wear and side to side movement which indicates a worn bearing, this causes the belt to not run true and chirp.