In the novels Tywin Lannister and Arya Stark never meet. At Harrenhal Arya was first sent to work in the kitchens, and then was chosen as Roose Bolton's cup-bearer, not Tywin's. She takes a glimpse at Tywin a few times, but never speaks to him.
The trivia items below may give away important plot points.
Arya's hit list is much longer in the novels. The full list is: Weese, Dunsen, Chiswyck, Polliver, Raff the Sweetling, the Tickler, Sandor "the Hound" Clegane, Gregor "the Mountain" Clegane, Amory Lorch, Ilyn Payne, Meryn Trant, Joffrey and Cersei.
According to the novel, Davos brought Melisandre by boat to Storm's End for killing Ser Cortnay Penrose, after Renly has been killed by her witchcraft. In the show, the two assassinations were condensed to one.