Translation:Did I commit a crime?
You are correct: the translation Did I commit a crime is perfective. It's asking about an event that is, from the perspective being offered, complete. In Klingon, it would have to be jIHeSpu''a'? As usual, Duolingo doesn't handle Klingon perfective correctly.
jIHeS'a' asks whether it is my habit to commit crimes, or if I am in this moment committing a crime.
jIHeStaH'a' asks whether I continue to commit crimes or continuously commit crimes.
Yes, but jIHeStaH'a' is asking whether I was committing a crime before now, still committing the crime now, and expect to be committing the crime after now. jIHeS'a' simply asks about now, without regard to before now or after now.
And when I say now, I'm assuming the time context of the sentence is now. If the time context is an hour ago, then jIHeStaH'a' is asking whether, an hour ago, I had already been committing a crime, was committing a crime at that time, and expected to continue committing a crime after an hour ago; jIHeS'a' would be used only if I were putting the listener in the vantage point of an hour ago; otherwise, if the speaker's vantage point is now and I'm talking about committing a crime an hour ago, I'd need perfective: jIHeSpu''a'?