There are certain adjectives in German that require the genitive in formal phrases, like: "jemandes/einer Sache ansichtig werden" "jemandes/einer Sache habhaft werden" "sich einer Sache sicher sein" "jemandes/einer Sache würdig sein" "einer Sache gewahr werden" In my opinion, these are very beautiful expressions. :) However, it doesn't occur very often that an object is expressed with a genitive. There are not too many of these phrases.

You've already answered your first question, it means "as soon as he saw the little prince". As to the case: Well, that's just how the construction generally works: Ich werde jemandes oder einer Sache ansichtig, überdrüssig, müde ... It's not very common nowadays any more, though.