Fundulus diaphanus is correct.
F.diaphanus is often confused with F.majalis, although they are rarely, if ever, found side-by-side due to diaphanus' preference for freshwater and majalis' preference for salt water and brackish estuaries.
I would probably feed it as diverse a diet as possible. Small inverts such as bloodworms, brine shrimp, mysid shrimp, and daphnia, plus some (mostly meaty) processed foods will probably provide a suitably diverse diet.
As previously pointed out, they are an opportunistic generalist, but they do feed heavily on other animals, such as aquatic inverts and small fish.
Like all killifish, they can be quite aggressive towards other fish, and can be difficult to safely cohabitate with other animals. But I think if you provide a proper diet, it should transition to captivity quite well. Killifish are extremely widespread and successful because of their versatile nature.