I don't recall if Arya heard about Joffrey's death, but I can assume that she did. There is no way she heard about Tywin Lannister's death, though, because there wasn't time for that news to reach her. She last saw the Hound dying, which explains she removed his name. read more
Ilyn Payne has not made an appearance in the show since the end of Season 2 (because of medical reasons in real life), but he's mentioned in the final episode of Season 4. His role in the books as Jaime's companion has been given to Bronn, so he's probably not going to show up again. read more
Arya has not stopped mentioning Ilyn Payne in her prayer. The Hound is the only one whom she omitted while he was alive. The list kept shortening as the people on it kept dying. read more
Ser Ilyn Payne: same as above; alive in the books, written off the show so dead. Gregor Clegane: capture of Arya and her companions; dead but partially reanimated. Sandor Clegane: Murder of Mycah; alive, but his name was removed from the list when Arya leaves him to die. Amory Lorch: Murder of Yoren; dead. read more