Absolutely let them out. Momma knows best and will guide them. I'm always surprised at how fast my goose mommas are walking their goslings around the yard when they hatch.

They are fine as far as their individual health goes, but as a group don't be surprised if a few show up missing every now and then. Chicks are a tempting target for hawks and other predators and momma can't save them all at the same time.

The run is enclosed on the top as well as the sides... no hawk will be getting my chicks! What about treats/scratch for Mom as well? Will a chick possibly get some scratch and choke on it? Should I give it to Mom separately? I have a slice of watermelon (seedless variety) that I thought they might all enjoy?

Go right ahead. None of it should be a problem.