Regarding the staircase, Balanchine may have been thinking of the Liubov Popova set for Vsevolod Meyerhold's Magnanimous Cuckold.
http://www.glopad.org/pi/en/image/902
According to Marilyn Hunt's Prodigal Son's Russian Roots (Dance Chronicle 1982), Meyerhold's "theory of of the importance of distinct 'planes of action'" were an influence Balanchine - and perhaps on Apollo. Hunt also says:
Quote
Balancine’s lifelong insistence that his dancers not emote but simply do his steps can be compared to Meyehold’s theory of movement being the source of emotion, as opposed to Stanislavsky’s method of working from the inside out, against which Meyerhold was rebelling.




