American English is my mother tongue. I also used this word order ("Do we have his books also?") as it sounds most natural and clear (i.e. Do we have his books in addition to other things?). DL disallowed that answer. "Do we ALSO have his books?" seems to imply that some more of "his books" may be in the possession of others," which to me is saying something different from the original German sentence. Please explain.
"Have" in this way is used for verbs e.g: "Have you collected the tickets?", "Have you done the homework?", "Have you read his books?"
In case of this lesson, "Have" is not used in terms of specifying "Tense", it is used to specify possesion e.g: "I have the pen", "They have books" etc
I said "have we his books too" which is the way we would phrase it in our country. So as well as a German test its also an English test half of the time. unfortunately Duolingo is a Grammar N*zi. But then again I understand non native speakers would not know to speak this way, but im sure native english speakers have this problem as I do.