As talented as Hendrix was...he was a sloppy player, well atleast the concert vid i saw...
Hmmm..Basics there are some classical pianist that play more than just classical.There are some that play Jazz and Blues better than hendrix could have ever played at his peak but they in that group of the unknown and are probably prodigies...Could some random blues player (guitarist) pull off chopins fantasie impromtu or one of those really really hard classical songs that Azreal has mentioned before??? probably not but their is a great possibility that one could..not saying its not possible
and i would say that classical pianist pratice on all four tihngs you mentioned...same goes for the blues player