Cooling fan not running, spins freely by hand. on 1991 Ford Taurus

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Wiring appears to have overheated, insulation melted/deteriorated, Black/Orange wire from motor not connected to anything (end stripped and bare, appears to have been connected at one time). (1) What does this wire connect to? and (2) What is probable cause of wire overheating.
(1) Answer
To address your wire question - the cooling fan motor has two wires going to it - Dark Blue and Black.

The black/orange wire comes out of the engine compartment fuse box, and goes to a splice - with two wires going into the IRCM (Integrated Relay Control Module), and one wire going into the fan resistor.

You probably need to assess the damage and repair all wiring, then probably have to replace the cooling fan motor, as it likely overheated.