It's not so much about what is in the table salt (called sea salt or no), although anticaking agents are likely harmful to your crabs. It is really about the nutrients that are required from the ocean salt. Enzymes, electrolytes, and other nutrients. It's also important to have a correct salinity mixture, hence the need to mix the salt according to package directions.
Please do take the salt you are using out of the tank. If you have used it to mist the tank or to soak the bedding, you will want to replace the substrate asap.
You may never really know for sure what caused the deaths of your crabs (Other than the molter), but you really do need to take care of this salt situation.
Also, the rainwater, in what do you catch it? Does it happen to run off the roof or anything? Down a drain pipe? Straight from the sky into a container?
Also, I don't see that you offer any calcium sources other than the shrimp? Your crabs need a very wide variety of foods. You will want to pick up some spirulina and kelp at the grocery store - you can find them in the bulk section of the natural foods, usually. Otherwise, you can order some good crab mixes online that contain seaweed and mealworms and other important foods your crabs need.
I'm afraid what you are feeding them is just not enough.

Try boiling an egg (save the shell when you peel it) and offering them the cooked yolk, and sprinkle the crushed eggshell on top. You can leave eggshell in the tank for long periods too, so maybe even leave it in all the time. Also, did you know that your crabs would LOVE a chicken or beef bone (like ribs) if you crack it open with a hammer so they can get to the marrow? I use a heavy marble rolling pin to mash bones for mine. It crushes them open and I just lay the half bone or chunk (small bones lol) in the tank. They love it.
Start using your imagination. Put a protein source in their food dish every time you feed them, and it's better to find some whole grain meals to replace the processed cereal you are giving them. The natural nutrients have been processed right out, and there is really not much left. you can also find some of those in the natural food section in your grocery store. Any grain, the closer to natural the better! You can even buy whole grains and grind them up in a coffee grinder.
Here is a great link to help give you some more ideas: Beginner's List