I see a number of issues here.
Informal ways to ask someone a question about what they've done, which is relevant now
For example, two people meet to eat some cuisine X at a restaurant, and one wants to ask whether the other has ever eaten X before. Full question would be "Have you eaten X before?". Informally, you may omit the "have you": "Eaten X before?". At a pinch, you could omit the "have" and say the "you": "You eaten X before?". (That last form might sound rather blunt to me, in some circumstances.) All forms of the question use the verb's past participle, not its past tense form. The question cannot be *"(You) Ate X before?".
Informal ways to ask someone a question about what they did in the past
For example A: I've just got back from Japan. B: Did you eat whale meat?
Full question would be "Did you eat X?". Informally, you may omit "Did you" or "Did", so the question would be "Eat X?" or "You eat X?" All forms of the question use the verb's infinitive, not its past tense form. The question cannot be *"(You) Ate X?".
So in each of the above cases the verb is not in the past tense form, but in some other form. Even informal short forms of the question don't use the past tense form.
The only way I can see "You ate?" as being a grammatically correct thing to say is if it's grammatically a statement, but said in a questioning tone of voice to make it a question. For example: A: I ate whale meat once when I was in Japan some years ago. B (astonished): You ate whale meat?
But I can't think of any situation where just "You ate?" on its own would be a sensible question to ask.
Now what, I wonder, is your poster supposed to mean? Perhaps the context is two people meeting, round about a mealtime, and one of them wonders if they need to eat right now. Then the question to ask is "Have you eaten?", though to my mind that might be a bit unclear, and I'd prefer if the speaker clarified what meal they're asking about, e.g. "Have you had lunch?". Informally, this could be "You had lunch?". However the question's phrased, the verb needs to be in the past participle.