Mystery snails are apple snails. The site
http://www.applesnail.net is the best web site on these snails which should answer a lot of your questions.
It can be hard to get the apple snail eggs to hatch in aquariums because the eggs are laid above the water line. Is that what you had? If not, then you don't have apple snails but some other kind of snail.
The baby snails aren't picky about food. They'll eat most fish foods including ones with plant and animal matter. They should have more plant than animal matter. Some species of apple snail eat plants while others rarely do. Both should enjoy algae and sinking plant-based fish foods such as sinking spirulina wafers and other foods made for plecostomus catfish. Some apple snails will eat various fruits and vegetables. Start with cucumber (split and deseeded) and maybe some romaine lettuce to see if they like either of those.
Baby apple snails grow pretty slowly, at least in an aquarium. The more room they have, the more food they have, and the warmer that it is, the faster that they grow. They should be kept warm, at least 70 degrees F. Your "tank" for them is very tiny. You'll need something bigger soon. I don't consider 3" (versus 1.5") to be deep at all. I would add more tank water to the baby snail container so they have more room in which to live. Apple snails can take in some atmospheric oxygen so they need to be able to crawl to the surface but I think "too deep" would be over 1 to 2 feet.
Adding a source of calcium is good for the snails to help build their shells. In addition to whatever kind you are using, cuttlebones, oyster shells, and crushed coral are all things that will leach calcium into the water.
It is normal for 10-20% of a batch of snails or fish that do actually hatch to die simply from things out of your control such as genetic problems, incubation problems, and so on. If you get 25% of the babies to survive, I would say that is very good. They will grow fast and eventually need 10+ gallons per apple snail so I hope you can find a home for them because I just know you will have a bunch survive!