Because, let's face it, every section needs one.
After the musical, when they're gone from Oz, the two run into the Doctor somehow. (Not sure which one, but it's likely Ten.) Elphie eventually gets killed. Fiyero, still a bag of straw, sets himself on fire; silly him, he did it in the TARDIS, and so he regenerates into someone who looks like Prince Edward. The Doctor kicks him out in Andalasia because he was getting way too angsty, and Fiyero takes Edward's place.
It's never explicitly stated in the show that he's from Earth. The closest we get is him describing himself as a "corn-fed hick", however it could be that he simply hails from the countryside of Gallifrey.
His other incarnations include AbbieHoffmann
's Mark Cohen.
The Leading Player is a Renegade Time Lord/Lady
His initial incarnation resembled Ben Vereen in the 1970s, but he has been able to regenerate countless times since, and has even become adept at changing his sex. The other Players are his Companions and the stage is his TARDIS, which explains how some of Pippin is set in Medieval France. He has no name and is referred to simply as "THE Leading Player" the same way the other Rogue Time Lords are. He displays Time Lords' typical lack of fashion sense with his usual outlandish outfits, and likes to get his dirty work done, but in true Time Lord fashion, doesn't like to get involved himself, but gets his Companions to do it while he observes. Upon staring into the Untempered Schism he was one of the Ones Who Went Mad and decided he was going to kill some humans in the most fun and amusing way possible.
Her business cards are psychic paper; they say exactly what she wants the person she's talking to to read.
The Father of the Rhinemaidens is a Time Lord
. He told his daughters to guard the Rhinegold, which is really Time Lord technology. The Ring could be created from the living metal Validium. The Tarnhelm seems to have TARDIS technology, shapeshifting, invisbility, and teleportation. Then Siegfried can understand birds and hear Mime's thoughts after tasting Fafnir's blood. Perhaps this is from Fafnir's years of exposure to the Tarnhelm, translation units and telepathy. Prophecies can be performed due to time travel, the idea of ruling the world could have come from looking into alternate timelines. Or what the Time Lord said could have been a stable time loop to destroy the Gods.
Sir John Falstaff is a Time Lord. That's how he manages to appear in Shakespeare's history plays set in the early 15th century, and in the screwball comedy The Merry Wives of Windsor
—despite the latter, by all appearances, taking place in Shakespeare's own Elizabethan period. He's a time-traveller, and ends up taking Prince Hal as his Companion because he can't resist the thrill of getting to hang out with a famous historical figure in his youth. His other Companions include Doll Tearsheet and Mistress Quickly.