No problem, excellent questions! Congratulations!
Leave the mom and her baby in there until the rest of the eggs hatch. She may stop sitting if you move her now. I've made the mistake of moving the nest too early and lost half the eggs.
Are they safe? Ducklings are predator attractants.
The baby doesn't NEED to eat within the first 24-48 hours, because it still has yolk reserves, but I would still put food and water near them. The water should be small enough that the baby can't get in and drown or soak itself. Ducklings get cold easily. (You shouldn't let ducklings swim unsupervised until they have feathers, also.)
As far as what to feed them, you should probably start with commercial chick starter as mash (not pellets). I think some people put electrolytes in the water, but this isn't necessary.
Mom will enjoy the baby's food and water, too.
