Barn in itself could mean either child or children (it is an irregular noun), but because of how it is used in the sentence, the singular version would require an article. "You have an unusual child" would be "Dere har et uvanlig barn" (Disclaimer: I'm not sure about the inflection of uvanlig here. I feel like it should get a T since barnet is neuter, but it somehow doesn't look right)
I would not get offended by uvanlige, actually (despite my earlier comment on "spawn from hell"), but if they said unormale I would get insulted.
Uvanlig can mean they are especially gifted and talented, unlike the regular (vanlige) kids. But if they are unlike "normal" kids (unormale = ikke normale)... I find it hard to imagine that as a neutral or kind comment.
It's not on the list. And after consulting my huge Norwegian-English dictionary I don't think it fits either. But I'm really not that particular about it (fnis). (There were plenty ways to use particular! That's why I like my books even more than I like online tools.)
(Here's the current list: uncommon, weird, unusual, atypical, peculiar, abnormal, strange, unordinary, extraordinary, special)
No - Duo seems to use children/kids fairly indiscriminately. In another translation I put 'children' and was told it should be 'kids', but the word was still just 'barn'.
In English, 'kids' is a lot more informal than 'children', but there doesn't seem to be any difference in Norwegian. I don't know if there is another word for 'kids' - if there is I haven't come across it yet.