"the dating relationship would be no contact -- no hand-holding or kissing" -- good (or that's what I'd think!).
She tells you she "[doesn't] belong in [your] home any longer because she ha[s] to fight demons every day and she belong[s] with her daddy, [the boyfriend's father]" -- not so good.
She comes to "believe certain objects including her teddy bears [are] possessed by demons" -- not so good, either.
The parents encourage her to leave your allegedly demon-ridden home and move in with them -- a class B misdemeanor.