"He eats the fish and the chicken."
Translation:O, balığı ve tavuğu yer.
O balığı ve tavuğu yer. = S/he (hidden subject) eats that fish and chicken.
O, balığı ve tavuğu yer. = S/he eats the fish and chicken.
"O" can be the 3rd person pronoun (he/she/it/that one), or the demonstrative adjective (that). In the latter case it has to be followed by a noun. If you need the former meaning, and it just so happens that the next word is also a noun, you put a comma so as to let the listeners know that it's dysjunct from the next word and it's not an adjective (= it doesn't mean "that" anymore).
without "O" is accepted. Can someone explain the difference between using it and not using it
it is just a matter if you want to emphasize the subject or not :) It isn't needed because you can always figure out the subject from the verb.
On Memrise I learned that chicken (meat) is "tavuk eti", just like the word for fish (meat) is "balık eti".
My question is this: If these are the terms for the food versions of the animals and they're not used in this sentence, does that mean that the man in this sentence is actually eating the animals raw??
No, it doesn't mean raw. You can say either "Ben tavuk yerim (I eat chicken)" or "Ben tavuk eti yerim (I eat chicken meat)."