Deskwriter cartridges are pretty expensive. So far I have never heard of anybody damaging his deskwriter by refilling cartridges. But HP doesn't recommend it. Also, the new HP ink is more 'water proof' than any kind of refill. It's better not to let the cartridge run completely dry, and you should certainly not let an empty cartridge sit on a shelf for some time before you refill.
Some people systematically add ink to their cartridges to ensure it never runs dry.
After a number of refills, the printing nozzles become blocked by dirt and the refill will not longer work. Usually you can expect about 3 to 5 refills. Sheaffers's Skrip Jet Black ink seems to please most people. Park Quinck Permanent Black. But any water-soluable ink should do.