The Haggadah was written during the Talmudic period, so I would expect it to be written in Aramaic. Especially since the entire purpose of the Haggadah is the telling over of the story of ...
Why do we sing "chad gadya" at the pesach seder? What is it supposed to be about? Also, as a side question, is it "d'zabin aba" or "dizvan aba"?