To your first question: yes it is possible. The difference is that
... était mangée is imparfait and
... a été mangée is passé composé.
Usage of imparfait vs. passé composé is a separate topic in itself which I can't answer exhaustively in a short post. There are several lessons on this topic on kwiziq, however. I suggest you either browse the Library or progress through the lessons until the start to appear naturally in your lesson plan.
Or, alternatively, if you're impatient, why not try Google?
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