"она написала короткий рассказ"? Or does рассказ already imply that the story is short?
Your answer is better. рассказ can be a story.
Рассказ generally refers to short stories when talking about literature. It can be used during informal conversation as a story (I want to tell you a story, for example).
I don't think I understand the difference between писала and написала
I'm with you. Рассказ translates as "story" in other exercises. Adding короткий shouldn't make the answer wrong.
Жаль, но буквально: "короткую историю" не приняло, хотя технически это тоже правильно.
Why does she pronounce з as с in word рассказ? Is there a rule behind this pronunciation?
It's called "final consonant de-voicing" г becomes к, д becomes т, and so on. You can Google the full list.
Where does "short" come from?
I put Короткую сказку. Wrong?
Сказка is a fairy tale.
Why is рассказа considered a typo?
Because it is
the word is рассказ
do we use nominative case in this phrase for "рассказ" ?
It's accusative, actually.