Does did you eat and have you eaten mean the same thing. Could I use either one. What are the rules?
A noble effort, Sevinj. It is not an easy question. 'Did you?' suggests that the speaker is only interested in the existence of that isolated past event, remote from today's reality. 'Have you?' emotionally/intellectually connects that event with now, over that span of time, so that the option still exists of completing the omission if it exists.

'Did you ever eat snails?'-- an idle enquiry.
'Have you ever eaten snails?" -- they are on the menu, shall we try them?

Still, a native speaker is liable to utter either, with the same intention.

PS: I want to add just a sentence or two more about this. We must again (as JTT never forgets) consider context. The 'did you ever' form would most likely occur alongside some more specific reference to that past time, as for instance 'did you eat snails when you were in Paris?', just as the the 'have you ever' form would likely appear at a restaurant or other current situation or topic relevant to now.
"did you "eat...?" supposes "back then when", that is a definite moment in the past.
Ex: -" I went to Japan last year."
- "Oh, did you eat sushis?"

"have you eaten...?" supposes "ever", that is at any time between your birth and now.

Hope it helps too!
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Hi, sqiovanni

I will try to answer to this question.

"Did you eat" means the action that took place in the past (from yesterday till years ago).
"Have you eaten" means the finished action at present (today).

Sorry, teachers, if I'm wrong.

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