Most "Ghost shrimp" (there are several species sold under that name) sold in North America are Palaemonetes paludosus. They do in fact breed successfully in freshwater. The young do not need special foods, such as green water to mature. RCS or Red Cherry shrimp are Neocaridina denticulata sinensis.
These two types of shrimp are not even remotely related. There is zero chance of interbreeding. They both do well in the same water requirements, and are extremely peaceful. They make excellent tank mates.
There are shrimp sold as Ghost shrimp that require brackish water to rear their larva, but they are rare.
A quick and easy way to tell if the species of shrimp you have require brackish water is the egg size test. If the eggs are extremely tiny, like Amano shrimp, then odds are very good that they need serious dedication to breed in captivity. If the eggs are similar sized to RCS, Snowball, CRS, etc... then they will either have benthic off spring, or a very abbreviated development cycle.