Radio waves are bad at getting through water, let alone into air. The Looking Glass might of been controlling the radio tower, and the radio tower was broadcasting the signal. This also explains how Ben was able to contact the station with his tiny radio. (Explains purpose of cable).
Its damage is purely coincidental or was already there when Rousseau arrived.
The Cable is part of an ELF Antenna used for secure communications with submarines and the outside world.
Though it appears outwardly to be a cable, it is a tube transferring oxygen, water, or some other substance between The Island and The Looking Glass.