In the reading exercise, the version without את is also marked as correct.
When is את optional before a definite reference ?
It is considered more correct to leave the את out, but it's very literary and no one does it. So you should definitely keep using it, but also bear in mind that it can be dropped in some contexts.
As far as I know, it's not considered more correct, and no one except Ben Gurion supported avoiding it (and he wasn't really an authority on Hebrew).
Maybe, but it's still used in some literary pieces and poems, and even sometimes in the media. This form appears in the Bible as well ("היהפוך כושי עורו ונמר חברבורותיו?" is only one example), so Ben Gurion definitely didn't just make this thing up.
All I'm saying is that it's not more correct to drop the "את", I'm not saying that it's always required (and I do agree with everything else you wrote, if it wasn't clear).
הילדים שמים את הסוכריות בחוץ
should also be acceptable.
put denotes present as well as past in english
מה ההבדל בין ״בחוץ״ ל-״החוצה״?