Does this short German sentences make sense?

Mittags habe ich Fisch und Eier gegessen. (At midday, I have eaten fish and eggs)
Mittags *** ich Fisch und Eier (At midday, I ate fish und eggs)

As John P says, the commas are unnecessary.

The sentence is otherwise totally correct colloquially. Mittags for the midday meal is right, and correctly written with capital 'M' at the beginning of the sentence.

However if you want to express it even better, perhaps in a written-down note rather than in a quickly spoken sentence in a casual conversation you could use:

Zum Mittagessen habe ich Fisch und Eier gegessen.

McGonagall

The comma wrong in both your English versions; the comma is not needed. I think "Mittags" is wrong, because it brefers to 'middays' in general, but await answers from Germans.

"Mittags" is correct. Mittags esse ich ein Butterbrot mit etwas Schinken, Kaese und Mayonaisse. Hm, hm, das schmeckt gut.

Man kann/sollte nicht jeden Satz Wort fuer Wort uebersetzen um den gleichen Sinn zu erhalten.
One cannot/should not translate a sentence word for word to keep the meaning.

This native Grandma resides in the beautiful State of NY