When Beckett questions the reasoning of why Castle wants her to believe in Mediums etc. he replies with: '... if you don't believe in even the possibility of magic you'll never ever find it.' He is paraphrasing a famous quote by Roald Dahl ('Those who don't believe in magic will never find it.')
The 'role' of the dead psychic is played by Patricia Tallman, the actress perhaps best known for her role as Lyta Alexander on the series Babylon 5 (1994). The Lyta Alexander character is a very powerful psychic.
The trivia item below may give away important plot points.
A bit of foreshadowing? When Castle is telling Beckett, Ryan, and Esposito about a psychic reading Viven once did for him, he was told that "a beautiful woman" would one day move into his loft and stay with him forever. While Castle believes Viven was referring to his mother, in retrospect it could refer to Beckett, who, after they get married, packs up and moves out of her own loft in Castle: Last Action Hero (2014).