RE: White Castle Fish/Chicken/ChickenRings?
I have checked every copy-cat and secret recipe site that I know of, and none of them have any recipes for White Castle except for their burgers. I suspect that their chicken sandwiches and rings are made of breaded ground chicken (like a chicken fritter), but beyond that I have no idea. If you are going to get a recipe, you will probably have to find someone who worked (or works) at White Castle, preferably in management.
As far as Church's Chicken is concerned, they are owned by AFC Enterprises, who also own Popeye's Chicken & Biscuits and Cinnabon. There is no mention on either Church's or AFC's website of any possible connection with White Castle and vice-versa, but that is really no indication that one can't exist. There is also a possibility that a person or company holding both companies' franchises in a given location is attempting to combine their two franchises to get additional business.
Sorry I can't be of more help.