"What did you say?"
I translated this as "nuq bIjatlh?", but I was told that I made a typo and that I should have translated it as "nuq bojatlh?". Why should I not use the normal "bI-" prefix here?
The bI- prefix indicates that the subject is "you" and that there is no object.
But here, there is an object -- the question word "what" is asking about the object of the verb and is grammatically an object.
So you can't use bI- but have to use Da- (when speaking to one person) or bo- (when speaking to several people), which are the prefixes for "subject = you, object = him/her/it/them".
When this lesson is presented in the format of "pick the right answer from three choices", the choices all have the first letter capitalized. Is that wrong for Klingon? Is that just a "feature" of Duolingo or the Android app?
That is indeed wrong for Klingon and is a "feature" of Duolingo which works well for pretty much all other languages but not for Klingon.
It's point 1c on our list of known issues: https://forum.duolingo.com/comment/26778885
Developers know about this but I'm not sure how far up on their list of issues it is to make a special case for Klingon here.
Can the "Da" always be left off for questions with "nuq..." or only in certain fixed expressions?
Only in the fixed expressions nuqneH? and nuqjatlh?.
You couldn't say *nuqbom? for "what did you sing?" or *nuqje'? for "what did you buy?", for example.
Also, nuqneH? is not fully interchangeable with nuq DaneH? -- it's an interjection, a reaction to somebody coming up to you, but you wouldn't use it to ask what someone will want in the future, or what they wanted at a specific point in the past. Similarly with nuqjatlh?.