"When does our bus depart?"
Translation:Wann fährt unser Bus ab?
abfahren = (to) depart
So could it be translated as "Wann abfährt unser Bus?"?
No. The prefix has to go at the end.
If not, how else could it be translated without having to have an "ab" at the end?
Whenever you have a separable verb like "abfahren" conjugated in second position like this, the prefix has to go to the end. That's simply required by German grammar. It's probably better to just learn that rule rather than trying to avoid it.
However, since infinitives don't move the prefix to the end, you could say "Wann wird unser Bus abfahren," which is a reasonable translation for this sentence. I would guess that Duo doesn't accept that though.
I'm not sure I understand your question. Nominative would respond to "wer" (or, in this case, "was"); accusative would respond to "wen" (or, again, "was").
But a better way to think about it might be to replace the English noun with "he" or "him." If "he" works, it's nominative, so use "unser Bus." If "him" works, it's accusative, so "unseren Bus." So "When does he depart?" -> nominative -> "unser Bus."
Essentially yes. In technical terms, the bus is the subject of the sentence. It's the thing that's doing the action-- it's the thing that's departing.
An accusative object would be the thing being departed; if I said "When does the bus depart the station?" then the station should be the accusative object. (I believe "abfahren" has a different meaning for its accusative object, so you wouldn't "abfahren" a station, but this is just an illustration.)
I don't think I can give you reasoning other than to say that question words like "wann/wer/wo" etc. always go at the beginning. Yes-or-no questions, on the other hand, put the verb first ("Fährt unser Bus jetzt ab?").
This is the same as in English: question-word sentences put the question word first ("When does our bus leave?"), and yes-or-no questions put the verb first ("Is our bus leaving now?").
(Also note the correct spelling of "fährt (/faehrt).")