"My favorite fish is the cod fish." "My favorite fish is cod." "Cod are my favorite fish." "My favorite type of fish is cod." These are correct. 'Cods' is incorrect, 'cod' is correct.

The above answers are essentially correct, in that several of your your answers are correct, but I thought I would add some specific subtleties for advanced use. To say you like the meat to eat, I think you would only naturally say " my favorite fish is cod". "My favorite fish are cod" implies that you like the fish themselves, not the meat specifically. "Cod is my favorite fish" is perfectly correct but sounds unnatural, so I would opt for "my favorite fish is cod", or just "cod" in response to a question. In common speech I think the "the" article is not necessary in this instance. This would be used more in a documentary or essay on cod. for example "the cod is a noble creature, which swims..."

yes, all of your choices are true, you can say i love cod fish, or my favorite fish is code and so on. good luck