Death in a bodysuit There are plenty of references here, but the most direct one is Ingmar Bergman’s The Seventh Seal. See also Persona and David Lynch’s Dune.
Painted face David Bowie’s Scary Monsters (and Super Creeps), as previously noted.
Skeletal angel wings on a pedestal Also David Bowie — specifically, the mid-’80s Glass Spider tour, which is a pretty dubious period to be borrowing from.
The shell bra Botticelli’s The Birth of Venus, obviously.
The hand bra Rolling Stone‘s famous Janet Jackson cover.
An anthropomorphic black swan A playfully surrealist take on Black Swan. There’s also probably a sly reference to Jeff Koons and his magenta swan, given how this coincides with a lyrical reference to his work.
Multiple faces Warhol’s Marilyn paintings.
Zombie bride Tim Burton’s Corpse Bride.
Zombie Marilyn Both of the above together!
A flat, stylized backdrop This is very reminiscent of any number of German Expressionist films — compare and contrast this image from The Cabinet of Dr Caligari, for instance. There’s also a distinct Der Steppenwolf/Magic Theater vibe to the whole thing — at one point Gaga appears in an oversize hat, and there are several instances of people/things disappearing in puffs of smoke.
Voguing Madonna! It’s not a proper Gaga video without at least one Madonna reference, is it?
Writhing on a mattress Madonna again, specifically Erotica/”Justify My Love” era. Never enough Madonna!