There is no episode with the eighth Doctor regenerating, he was only in the 1996 movie, and when the show returned in 2005 it was with the ninth Doctor.
Season 3, Episode 3: Gridlock
The episode title is "Smith and Jones" it is the first episode (not counting specials) of the 3 season (David Tennant's second season). It is the episode when the Doctor is in a hospital that gets transported to the moon by the Jadoon. The doctor meets Martha Jones who is studying to become a medical doctor and they hunt for the old woman who the jadoon are after.
I don't recall a "new" Doctor Who episode in which a man screams for a long time, but there is a Torchwood episode this happens in. Season 2, episode 11 "Adrift"
The first episode of series 3.
Peter Kay appeared in the "Love & Monsters" episode of Doctor Who, which is episode 10 in season 2 of the revived series (2006).
There is no definitive information about William Hartnell's favorite episode of Doctor Who. However, it is documented that he was proud of the show and his contribution to it during his time as the First Doctor.
Army of Ghosts (two part season finale)
Charles Dickens appeared in the Doctor Who episode "The Unquiet Dead" which aired in 2005 during the first season of the revived series. He was portrayed by actor Simon Callow.
Matt Smith first apears in the last episode of season 4, episode 18, "The End of Time (Part 2)" and returns in the first episode of season 5 in "The Eleventh Hour."
He's shot by an astronaut in Season Six Episode 1.
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