The picture of young Norman in Norma's bedroom is an actual picture of Freddie Highmore when he was younger.
Norman (Freddie Highmore) is seen using his taxidermy skills on an owl. The same owl (although faded with age) is seen in the parlour scene in Psycho (1998).
When Romero tells Norma about the shower curtain rod being broken and later tells Norman how it broke, it is a reference to Psycho (1998) as Sam and Lila find no shower curtain in the motel room while investigating Marion's disappearance, unaware that Marion tore the curtain down as she was fatally stabbed repeatedly by "Mother."
When Norma (Vera Farmiga) finds Norman (Freddie Highmore) placing his taxidermy around the living room she has a similar creeped out body language that Marion Crane (Janet Leigh) has when she sees the taxidermied owl in the parlour scene in Psycho (1998).
The film that Norma suggests to Norman that they go see together and then the latter later watches alone is the 1944 psychological thriller film noir Double Indemnity, which is about an insurance salesman lured to his doom by a predatory femme fatale, a parallel to the close relationship between Norma and Norman.