Why is it 持っていません instead of ありません in this case?
Probably for consistency in Duo's teachings. I agree ありません sounds more natural here, but I also suspect many people would get upset that that doesn't literally translate to "don't have" as they know it.
Wouldn't 車 be way more natural than 自動車?
Yes, "jidousha" is more like automobile while "kuruma" is the normal word used for car. Just have to keep on submitting error reports.
車がありません should be accepted, reported.
'why does もっている use を instead of は？