I know where are her things is marked as wrong. Why?
The word order sounds unnatural to me. That might be the reason. If so, it's probably connected with the fact that "where are her things" is a question, but "where her things are" is something else (noun phrase?).
Yes, in a clause like this you have to use a different word order:
Where are her things? I know where her things are.
What is his favourite food? I know what his favourite food is.