Why is jedzącego in genative? This entire section is very unclear to me.
The participle behaves just like an adjective, and it describes the penguin. As penguin is in Accusative here (because of "widzieć" = "to see"), so is the participle.
Genitive would look the same in this example. "Nie widzę pingwina jedzącego rybę".
Follow-up: why is ryba in accusative? What is it the direct object of?