in my opinion, this is a little more formal than is common. Seems like the first three words would suffice
Yes, but the solution sentence extends with more hanzis. 他不在 is the short form of the same meanings. This is also correct.
Unfortunately 他不在 is marked as incorrect
It suffices in most cases, but still it depends on the context. e.g. If the sentence is used in clarifying that the subject is not here but would rather be in one or more other possible locations, then you need to mention 這裏.
The word bu zai has no audio