How many hours of music approximately exist today if every song ever
recorded in the world were counted - or to put the same question
differently, how much storage would a person need who wanted to
archive in mp3 format every piece of existing recorded music?

Are you intending to include all genres of music - classical, folk,
rock, Broadway shows, etc?   I presume you'd include multiple
recordings of the same music by different artists.  Are you asking
only for music that is "in print" today, or all music ever recorded?  
(By "in print" I mean available for purchase as a new recording.)