Change the blower fan speeds to see if the noise changes. It is possible that the fan is still running while the heat is off, and the fan is rubbing.
The starter or battery cables/terminals are corrode.
Low battery voltage .?
the clutch on your A/C compressor needs to be replaced.
Burried behind the dash on the passenger side, good luck.
some possibilities are. low coolant level, open thermostat, pluged heater core,
The head gasket is about to blow.....Typical ford..
Anti-rattle clips not installed properly
How do I replace the block heater in my 1998 F150 4.6L?
I don't know about the outside diameter of the hoses but, the outside diameter of the heater core inlet and outlet tubes are 3/4" (inlet) and 5/8" (outlet).
Low coolant? Defective thermostat? Heat control cable not adjusted properly? Heater core plugged or airbound?
Is the 1997 F150 Transmission is the same as the 1999 Expedition
The heater flap, or blend door, is difficult to replace with OEM parts supplied from Ford. There is an aftermarket kit that makes the job and cost significantly easier at heatertreater.net or on the Ebay listing.