Electronic – Would an inductor and a wire in parallel have an equivalent inductance of 0

It sounds like you're dealing with a SPICE simulator.

In SPICE, you define a transformer as a coupled inductor, with the following ratio:

\$\dfrac{N_1}{N_2} = \sqrt{\dfrac{L_1}{L_2}}\$

There's also a coupling factor K that comes into play.

The magnetizing inductance of a transformer is the inductance you measure across the primary winding with the secondaries open-circuit (floating). It's a function of the core material and geometry, air gap and number of turns.

Your \$L_1\$ and \$L_m\$ should be one and the same.

A negative value of inductance tells me the net impedance you measured is capacitive. If you are measuring cable inductance try measuring end to end rather than across one end. This answer presumes it is a multicore or coax cable you are trying to measure.

If your measurement system uses 1 kHz to determine impedance, an apparent inductance of 1.39 H would be an impedance of 8734 ohms and an 18.2 nF capacitor would produce the same "value" but phase shifted by 180 degrees hence giving you a minus sign for inductance - try switching the measurement equipment to "capacitance" to confirm this.

10m of cable would therefore have a capacitance of 1820 pF per metre. This sounds a little high so maybe the test frequency used by your measurement equipment is more like 3 kHz.