Does my Carbonite Cousin need feeding?
1 Does my Carbonite Cousin need feeding each harvest that he's not in my house?


No.  He's frozen in carbonite.  As Threepio says "He should be quite well-protected -- if he survives the freezing process, that is."


  2 Does he still take up a space in the house (e.g. for family growth)?


No.  As Han Solo said, the point is: "To freeze a being solid, then hang him on a wall like some trophy?".  Wall art doesn't need a bedroom.


  3 If the game ends before he is rescued, what is his status? Does he still count towards my people score at the end?


No, as Leia says: "He's trapped in that thing forever unless somebody releases him."

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