What about "You are coming with me?" (it was rejected - e.g.: "You are coming with me? I thought you were going with him!"). In general, if this is "Are you coming with me?": does "העם אתה בא איתי?" exist and if so, what would be the difference?
It should also be accepted. האם אתה בא איתי means practically the same, it's more formal and it also makes it absolutely sure the sentence is understood as a question regardless of your intonation.
I translated the sentence, ?אתה בא איתי, as "Will you come with me?". The correct answer, per the program, is "Do you come with me?". Why is my answer incorrect?
You used the future tense, while the Hebrew sentence was present.
Will you come with me? = ?תבוא איתי
Are you coming with me?/Do you come with me? = ?אתה בא איתי
do you come with me? really, bad english. Propper translation should be are you coming with me? Please fix it!
Well, not really a bad English. Just daily use makes the sentence sound a little bit awkward. Grammar-wise, it is correct.
(Consider the act as routine instead of near-future: do you (always) come with me before I lost my memory?)