A minute or so with the cable and a multimeter will tell you if:
1. The center terminals at the two ends are connected.
2. The outer terminals at the two ends are connected.
3. The center and outer terminals are *not* connected.

If these conditions don't hold, it's the cable.

The type of wire and the impedance are not particularly important in this application except that he may pick up hum from any power cords or transformers nearby. The wavelength is far too long at the frequencies of interest for impedance matching to be important.

Twisting the wire will help reduce pickup of unwanted signals. One turn per foot should suffice.