Yes, she comes from a pure blood family. it is stated on harry potters wikia that she is indeed a pure blood. Also most of her family is in ravenclaw.
Wrong. Her blood status is either pure- or half-blood. And Luna is the only known Lovegood whose house has been revealed, allthough her father seems to support Ravenclaw, too.
Yup, Luna is indeed Pureblood witch because her father names Xenophilius is the editor of Quibbler and her mother experimented the magic before Mrs. Lovegood killed herself. Her father Xeno is well known wizard in the wizarding world for sure. Therefore, Luna can't be Muggleborn indeed.