Well, neither Zest, nor the Wolkies were
Church Knights. I think you still fail to notice that there is a distinction between "Knight" and "Church Knight". Knight is anyone who practices Old Belkan system with emphasis on close combat. Church Knights are an organization serving the Saint Church--they represent it, so whenever people speak with Carim, they see the institution she represents in her, and pay due respect. That said, I don't deny the possibility that Carim is a knight commander or something of the like, it's just that her position in the hierarchy of the Church has never been established past hints.
No, I think she would be less of a missionary and more of a papal legate in modern terms.
Well, those are just fics.
Nope, not to my knowledge. Technically, the head of the church is Saint Kaiser Olivie (since she is their God), but since she is dead... except she is not, so meh.