Can a Djinn host a Parasite?
No, a card can't be hosted on two different cards at the same time. From the Netrunner FAQ on Fantasy Flight's website:


  Can the Runner install Parasite on a piece of ice but host it on 
  Djinn?
  
  No. A card or counter can only be hosted in one place at a time. 
  Parasite has the restriction that it must be installed on a piece of 
  ice, and therefore it cannot also be hosted by Djinn