I see stories starting with "Eines Tages,". Why is it not "Ein Tag"? Is "Eines Tages" a genitive form here? meaning "Of one day"? I am a beginner on German.
Eines Tages does, in fact, mean roughly "of one day," which requires the genitive (not "generative" case). And that because it is a reference to one particular day. The idiomatic English expression is "once upon a time."
You would use "ein(en) Tag" to refer to a "random," or unspecified day. "Ich brauche einen Tag nach Berlin zu fahren." (I need one (random) day to drive to Berlin.)
Eines Tages is a fixed phrase meaning some day or once. It's in genitive but analyzing this further won't help you. You may ask "whose day?" and the answer would be "once". Remember it as a phrase:
Eines Tages habe ich meine Schlüssel verloren.
Some day I lost my keys.
This use of eines Tages is typically introducing stories. Eines Nachts is also possible:
Ich wachte eines Nachts auf und meine Frau war einfach weg.
Some night I woke up and my wife was simply gone.
There is another use of eines Tages which refers to the future instead:
Du wirst mir eines Tages noch dafür danken.
You will be grateful for this some day.
It's uncommon to use eines Nachts that way, it would be understood as word play.