Åt du min apelsin? would mean Were you eating my orange? so it's a question of what you want to say. A better sentence than the one above would be Har du ätit upp min apelsin? (particle verb, stress upp) which would be more natural in Swedish – if you eat an orange, we generally consider you to have finished it. (and if you haven't, we'd prefer to say Har du ätit av min apelsin? instead).
Actually here is a gd explanation for the grammar. I hope it is the same in svenska http://www.edufind.com/english-grammar/present-perfect-vs-simple-past/
That description might be even truer about Swedish than about English. There is a tiny difference in how we use the past tenses (which only happens when English does not behave like in the description you linked to) but that is a too advanced topic for this course. So as long as you use the same past tense in Swedish as in English, you won't go wrong. So did you eat would be åt du.