I think you're thinking of nitrate when you say that a 0 reading is almost impossible, because for nitrate, that's absolutely true in freshwater tanks. The nitrate isn't converted to anything, and so we have to remove it through water changes. I try to keep my nitrate under 20 because I'm paranoid of things I cannot see (LOL) but everyone has a different philosophy on this. Either way, though, yes, nitrate is acceptable and will always be present.
The nitrite, which is what you mentioned earlier, is different. It's the product of converted ammonia, and it's still toxic. The nitrite is what is converted into nitrate, so nitrite should be zero in a cycled tank, just like ammonia.
I don't think the water changes are too large. Is your tap water pH the same as your tank's pH, or do you adjust it before you put it in the tank? In either of these cases, you'd most likely be fine, as long as the water was dechlorinated, of course. If the new water is drastically different, chemistry-wise, than the tank water, then this might stress the fish if you did a large enough water change. Conditions in the tank would be constantly fluctuating. But, I doubt this is the case.
And I still don't know what the heck could have caused that initial wound. But, the fact that you say some fish get it and it goes away, but this fish has gotten it and it's worse and infected, makes me want to say just keep your water quality pristine until you pin down the cause of this, and you should be okay. It sounds like the other fish made it through all on their own, due to good tank conditions and their own immune systems.