Hum at shut off is normal
There's a butterfly plate in there that shuts off airflow at engine shutdown to prevent a shuddering shutdown. The butterfly plate also closes part way when EGR is called for and the EGR valve opens. This is so the engine will suck in exhaust gas when it's called for. If your getting exhaust out of the FCV where the hose attatches the the EGR valve may be stuck open. They can be cleaned.
The EGR valve is on the drivers side of the engine rearward of the FCV.
You can see the butterfly valve in the Flow Control Valve (FCV) with the charged air hose off. With the engine shut off it should be spring loaded open and you can reach in and close it and it should spring back open
