Most minnows sold in your area are actually from brackish water. They can really only survive if given salt in their water and placed in a large, highly oxygenated aquarium.
Box turtles will eat pre-killed minnows. I supplement all of my box turtle species with minnows from time to time. I always fully freeze and thaw them first, as they're notorious carriers of parasites. I wouldn't think that a Box turtle would be able to catch a live minnow.
The Box turtles that I kept when I was a child ate toads. I began to place toads in their enclosure because I thought that the toads would help to keep bugs at bay. Each time I placed a toad from my yard into the enclosure, it was never seen again. Despite high walls that were partially buried, I assumed that the toads either dug or jumped out. I was shocked to watch one of my Box turtles viciously chase down, corner, and grab the leg of a toad nearly as quickly as I dropped it in. I've always had a fondness for toads, so I rescued the little guy and never tried to establish a "bug control" since. I'd assume that in the wild toads would have a much better chance of escaping a Box turtle. With their extreme jumping ability, I wouldn't think that a Box turtle could ever catch a ranid frog. Although, I'm sure they'd eat a sick or deceased individual.
