What is wrong with "A fiatal arab fiú ebédel, ahol a japán szakács áll?"
That's not how it's said in Hungarian. You need "ott".
In the right circumstances, could you also use "itt?"
I can't think of any sentence where it would sound right to me but I don't rule it out completely.
In my opinion It's ok. "itt" or "ott" are not absolutely necessary to use in this sentence.
it's not just necessary but mandatory in this case, since the entire point of the sentece is to show that the two actions are happening in the exact same physical location.
is it ok if the 'ott' is after ebédel instead of before?
Yeah, if you want to emphasize that the young Arab boy is the one who is standing there and not any other person. The original sentence emphasizes the place ('ott').