it should be: "nincs ott a szék"
and that comes from a native speaker.
That's just something else. "Nem ott van" implies it's somewhere else, "nincs ott" simply denies that it would be there - it's quite possible that the chair is lost altogether.
Why can't I say "A szék nem ott"?
You can say "A szék nincs ott." Take a look at this comment to learn the difference between 'nem ott van' and 'nincs ott.'
You wouldn't have a verb in the sentence.
Which wouldn't be a problem in the case of "Ott a szék", though. So this may not be a convincing argument.
True. I have no ideo why, bit feel an implicit "van" in your example, while in the question's example I have a feeling that it's missing something. I hope someone gets around who knows what's up with that :D
Mert ez így nem teljesen érthető. Kell hozzá egy létige is hogy értelmes legyen.;D
Why Ott and not Oda?
Because it's about position and not direction. "Oda" is like "to there", if we really want to make a difference.