How are the other fish looking and acting now? This, honestly, is a tough one because the 2 "sick" fish are now dead and I haven't heard of any other fish showing any symptoms. I am still stumped on the test results showing 0 nitrate. By this time the tank should be cycled and showing "something" for nitrate, even if it is low, just because there are fish living in the tank and there is food going in.
The bent spine you mentioned could have been caused by a number of different things, and again... with everything you have posted, I can find no solid explanation to offer you at this point. I took the opportunity to look at your aquarium photo, and I don't see enough plants in there that I would expect them to consume the entire nitrate content in such a set up. It takes a lot of plants to use just a small amount of nitrate... so honestly, at this point, I am sorry but I can't offer you any solid answers. At best I could take a few guess's based on the given info.
If I were to guess, I would say it is possible there could be a bacterial infection or a protozoan infection that hit the fish... either of those could produce the symptoms that you described in those species of fish. I see no solid evidence either way which of the 2 it could have been, and without current fish showing any symptoms, I'm going to advise you to just keep a close watch on the tank for a while.
If you notice any changes in the fish, however subtle and trivial they may seem, please post them. Please don't add any type of medication at this time. If you were to put the wrong med in there now, it would very likely do more harm than good.
Also, if any of the other fish begins to show any problems, try to get a clear pic, as close up as possible, of the sick fish. Pictures often make all the difference in the world, especially when trying to diagnose an unknown illness via internet. (working online as I do gets very frustrating because without the ability to run the proper lab work.. all anyone can do is make an educated guess) While some of us have enough experience to recognize many common illnesses, and to properly identify a problem enough to treat it safely and effectively, situations such as yours can be quite frustrating.
Your water test results... I have to admit that I am a little baffled at the straight line of 0's. Even in my own tanks there is at least a 5 - 10 reading for nitrate, which is to be expected. Do you have carbon in your filter? How often do you change the carbon? Also, I'm wondering, when you do water changes, how much water do you change each time? And one last question... how old are your test kits? If you have the ability to take your water in to a lfs and have them test it, just to compare the results, that could be a big help. If they confirm what yours read, then I would feel more confident that those numbers are accurate. It's very rare to find a system that is so completely and perfectly balanced.
I'm sorry I can't be of more help to you at this time. I can't always get here every day, but I will keep a watch over this thread and continue to help in any way I can. Oh, and before I go I want to mention... after rereading this thread from the beginning again tonight, having a cory for a few months is not something I would consider "a long time". When we are dealing with a fish that has an average life span of 7+ yrs, a few months is a very short time.
I still consider a fish "new" to the system for the first 6 - 8 months, as that is how long it can take for some problems to present themselves and for a fish to really settle in and adjust to everything new in its changed environment. Even people take that much time to fully settle into a new lifestyle/living arrangement. I am not trying to be rude or insulting, so please don't feel offended by my comment. This is just something I felt important for you to know. If you should run into a problem in the future, be sure to again list a time span that you've had your fish so that we are able to identify how "new" a fish is to the situation. That can help eliminate or identify certain problems. I was so glad you listed a time span this time, thats something many people don't think about when posting.
I hope from this point on things clear up and go well for you. I think you have a great tank going and hope you'll post pictures as it changes/grows. I love to see how things progress in other people's tanks as much as in my own.