Trey's fictional character:

Todd Anderson, Ethan Hawke's character from Dead Poets Society

Rick's fictional character:

Isaac Bell from Clive Cussler's novel The Chase

Nancy's fictional character:

Raskolnikov

Mike's fictional character:

Lindsay Weir. Tim from The Office. Benny Profane.

Tim's fictional character:

Optimus Prime

Amy's fictional character:

Dawn Weiner from Welcome To The Dollhouse.
(I'm so embarrassed)

Tom K's fictional character:

John Anderton

Cordelia's fictional character:

God

Brian's fictional character:

Charlie Brown

Chelsea's fictional character:

Anya from Buffy the Vampire Slayer

Henry's fictional character:

Ivan Denisovich

Wayne's fictional character:

Michael Bluth

Amy's time travel:

Kool Herc's Cedar Park parties in the West Bronx, summer 1974

Brandon's time travel:

I’ll take Germany in 1924 to perpetrate the small, unnoticed poisoning of a loquacious art school drop-out

Ethan's time travel:

Philadelphia, the week of the 2008 Phillies championship