Learn Turkish: Öğle yemeğinde balık yiyoruz.

"Lunch" in Turkish is a compound made of öğle (noon) and yemek (meal). To link them, yemek takes an -i ending, and its k softens to ğ, forming öğle yemeği. To say "at" lunch, we add the location ending -de. But when adding a location ending to this kind of linked word, we must use a buffer n in between, resulting in öğle yemeğinde.

Why doesn't balık have an ending to show it is the object of the sentence?

Because we are talking about fish in general, not a specific fish. In Turkish, if you were eating "the fish" (a specific one you already mentioned), you would add an ending to make it balığı. But for general, non-specific objects, the word stays in its plain form and usually sits directly before the verb.

The root of the verb "to eat" is ye-. Why is it spelled yiyoruz instead of yeyoruz?

When the present continuous ending -yor is attached to a verb root ending in a or e, that vowel "narrows" to ı, i, u, or ü. Here, the e in ye- changes to an i, making the word yiyoruz instead of yeyoruz.