I'm completely floundering with the articles. (The, a, etc.) there must be rules but on the basis of what I'm shown, there is no way I can figure this out.
Does "κότα" specifically refer to the animal when it is still alive and "κοτόπουλο" means that it has been killed for meat for human consumption? (like "hen" and "chicken") or are both words valid for "chicken"?
No, κοτόπουλο is any chicken, male or female, alive or not, whereas κότα is the hen and κόκορας the rooster.
Αχ, καταλαβαίνω. Ευχαριστώ!