OK, so we know what's wrong. You threw away the gravel which destroyed part of the filter in this tank, and in doing so allowed ammonium and nitrite to go up. This in turned killed your fish.
A 10 gallon hexagon tank comes with a built-in undergravel filter, if I am not mistaken. There's an air pump that draws water through the gravel, and in doing so, the water is cleaned. If you remove gravel, you're basically taking away filtration capacity. You should have about 6-8 cm of gravel. Anything less won't do the job.
Now, cleaning an undergravel filter is important. Once a month, use a chopstick or something similar to gently stir the gravel while you siphoning out the water. All the crud will be sucked away, but the bacteria in the gravel will be unharmed. Never, EVER wash the gravel in anything other than aquarium water. So while it is fine to take the gravel out and rinse it in a bucket of water from the aquarium if it gets really dirty, washing the gravel under the tap (faucet) is VERY VERY bad.
Throw away the salt or use it to de-ice the driveway. Serves no purpose in a fish tank.
Dropsy is a symptom not a disease. It is basically incurable on small fish, though sometimes they get better by themselves. Provided water conditions are good, fish as good as never "catch" dropsy so don't worry about it for now.
In the meantime, do not overfeed your fish. You only have 15 babies left, right? They should be fine with minimal filtration since they are so small. Provide tiny amounts of food. If any hits the gravel, you've fed them too much. With baby fish "little but often" is the way to go. For 15 newborn guppies, even half a flake, ground up, should be oceans.
Don't think of adding anything to the aquarium. Not plants, not snails, not catfish, not anything. Just top up the gravel, and then let the thing settle for at least a month. The nitrites and ammonium should drop quite quickly since the tank isn't completely new, but still, don't push your luck.
Cheers,
Neale