"What does the child eat?"
Translation:Mit eszik a gyerek?
'Mit a gyerek eszik?' is wrong? I thought the word order could be either way.
The verb has to follow the question word. "Mit eszik a gyerek?" or "A gyerek mit eszik?" -- these are the only possibilities here.
Is "Mit eszik a gyerek?",
the undefinite Conjugation form, of the 3. Person Singular?
Is it "eszik" instead of "esz", becaus of the "ik" form of "eszni", which says that it is "eszik" instad of "esz" in the 3. Person Singular (Ö)?
Eszik is the 3rd-person singular indefinite form, yes. The form that you find when looking up the word in a dictionary. (It's also the 3rd-person plural definite form, but that doesn't apply here.) Eszik is one of the so-called "-ik" verbs ("ikes ige") which all get an -ik as the 3rd-person singular indefinite suffix.
"Esz" doesn't exist in Hungarian.