Does Unknown's special ability still work after revealing?
In our group I must admit we never thought of giving Hermit Cards to revealed characters. We took the description in the rules too seriously I suppose:


  Hermit Cards help you to identify the characters belonging to the other players.


This being said, a quick check confirms that the rules don't mention you must give it to an unrevealed character. So the revealed Unknown can be given a Hermit Card and he can lie to choose the effect he wants...

Note that only the player who gives the Unknown the Hermit Card will actually know that the Unknown lied as the rules also say:


  The player who drew a Hermit Card and the player who was given the Hermit Card are not allowed to tell the other players what was written on the card.