That data helps. On the GH, that is indeed hard water. 367.5 mg/l is the same as 367.5 ppm, which is approximately 20 dGH. The ppm and dGH units are the two most commonly used in the hobby. This level of mineral will cause issues for soft water fish, like the tetras especially, over time. The calcium (primarily) dissolved in hard water is filtered out by the fishes' kidneys, and the calcium slowly blocks the kidneys and the fish dies. So this is likely part of the issue, long-term.
Nitrates are very high for fish, and even 50 ppm is high for humans. More regular water changes--at least half the tank every week, vacuuming into the open areas of substrate to remove as much detritus as possible, along with keeping the filters clean will all help to lower the nitrate occurring in the tank. Other members have dealt with high niotrate in the source water, and I will leave it to them to explain methods. AbbeysDad is one who has overcome this issue.
The fish deaths un-noticed would have increased ammonia and then perhaps nitrite, and these two forms of nitrogen are much more rapidly dangerous than nitrate so more likely a possible reason for sudden fish deaths. It is usually easy to see the beginning signs of ammonia or nitrite poisoning; increased respiration, fish closer to the surface and eventually gasping, red gill areas (in live fish), gill covers extended--all this is because the fish are attempting to get more oxygen but can't. Nitrite also inhibits oxygen take-up in the blood, making things worse still.
More frequent and substantial water changes would likely have compensated for the ammonia/nitrite. It is again a question of prevention rather than reacting to the deaths. I think it safe to assume the deaths resulted from all this combined. Live plants haven't been mentioned, but if they are present, especially fast growing species like floating plants, this can be a big help dealing with increases in ammonia, and that of course means no nitrite, and lower nitrate resulting.
Byron.