What damage could exist? There are two different ways these are made. Some manufactures the cartridge has the print head built in (like HP and lexmark). Some cartridges are only tanks and the printer has a separate printhead. With some aftermarket ink the printheads will clog up. Also the equipment used and the process used is important. The worst damage will happen to the printhead which in most cases is the cartridge itself. Epson printers are bad for the printhead getting clogged even with oem inks. Espon have to been ran constantly as letting the printer set for a week will sometime render the print head useless.
Printer Warranty? As long as the inkjet printer is not damaged due to the aftermarket cartridges the manufacter CANNOT void your warranty. Some say they will but it is in fact illegal for them to say that although the law does not reconized what they are doing due to uneducation about the industry. It is only a scare tactic to get you to buy only their consumables so that they can control the entire market.
It the quality of aftermarket inks good? Unfortunately I must say the inkjet remanufacturing industry is not very good. They are only a few good manufactures. Most have a 20 to 50 percent defect rate and only a few have a good 1 to 2 percent defect rate. It anyone wants to find a good ink I could tell you where to get it. Understand that I do not manufacture inkjet cartridges and only sell retail as I am not trying to solicitit here. I can tell you the manufacture though. I have try just about all of them and it is terrible. There are testing standard being developed right now to help produce better product. It will help to make each manufacture either do it right or not do it at all.
One Note: Most of the problems are with cartridges that have built in printheads. Most of the tank cartridges will work without problems. Also you could refill yourself at home, but becare that not all inks are good an that definetly inks are not compatible will all types. If you refill yourself besure to refill it BEFORE it runs out. This will help prevent the printhead from drying out.
I am not an expert of inkjet technology, I am an expert in the eletrophotographic process of laser cartridges. The toner cartridge industry does well and there are repeatable test standards in place to qualify components and to benchmark against oem cartridges for consumer information. When buying laser cartridges ask if they can provide you with ASTM F 1856 and ASTM 2036 documentation. If they don't beware.