It does seem sort of out of place on this show, but real world cops consult psychics/mediums all the time.
I agree. They made a big deal out of her making that story up last season and now they tell us it's true. I can't stand the character's attitude so I really don't care what her backstory is, but Anthony's line at the end was hilarious!
I also can't stand Witten so if this is how they get rid of her, I'm fine with it even thou I think the reason she got suspended is total BS.