What are the conditions that result in magnetization of a cartridge? Is it hours of playing time, months- years, both, or what?
That's a controversial topic. Some argue it's impossible for any part of a cartridge save the magnets themselves to become magnetized, since they're made of nominally non-magnetic materials. Others argue that trace impurities or other factors could allow magnetization. I avoid the "why" and "how" arguments, since I lack the scientific knowledge to contribute anything useful.
Much less controversial is that something, somehow changes after de-magging, whether with an active device like yours or the Cardas record. (Some have stated that once you actively de-mag you must do so more and more often, and that doing so progressively weakens the magnets. Thus the warranty issue.) The LOMC's I've owned (Shelter, ZYX) have all benefitted from a monthly (or so) pass on the Cardas LP. I've not noticed any need to "treat" the cartridge more frequently, so IME the Cardas LP will not harm the cartridge or shorten its life, beyond the few minutes added to total usage of course.
What are the audible signs that it needs to be demagnetized?
Until you know the sound of a cartridge in your system well, it will be difficult to notice. Nothing goes downhill suddenly. There's just a gradual diminution of inner detail, microdynamic subtleties, and "life". Everthing gets slowly more bland and boring. It sounds like playing with excessive VTF or excessive antiskating, the livliness is squashed out of the music.
Five minutes on the Cardas LP and everything comes back. It sounds like you cleaned the windows.
Doug