Is a captured unit considered to be in play for the purposes of uniqueness? For example, Boba Fett captures Luke Skywalker. Can the LS player simply play another copy of Luke or does he have to be rescued first?

Captured cards are out of play (see plage 27 in the rulebook) and are thus no longer counted as representing whatever is printed on it. After capture the card is simply a "captured card", nothing printed on the card has an effect once it's captured.

So, you may play the same unique card again.