Its just the music of Rage Against the Machine in general that hes making fun of.
That is not a Weird Al song.
Weird Al NEVER made a song about Barney on fire.
Avril Lavigne's Complicated
its a parody of "Ridin" by Chamillionaire
"I Want it That Way" by the Backstreet Boys
"Piano Man" from Billy Joel.
He made a parody of "Bad" by Michael Jackson.
It's not making fun of a particular song. It's more just in the style of the 50's "Doo-wop", Elvis type sounds.
Black Gold Soul Asylum
Weird Al never does a parody of any song unless the musician who wrote that song gave him permission. So he was clearly not punished at all for that parody.
It's an original, not a parody. However, originals are often in a song style of another group. This one is like Guns 'N' Roses
It's a parody of Coolio's song "Gangsta's Paradise."