From the rulebook:
"If at any point during the game a player cannot draw cards because the Enterprise Deck has been depleted in this way, the players lose the game!"
I interpret that to mean if it is your turn to draw a card and you can't because the deck is empty (and there are no cards in the discard pile to force a reshuffle), then you lose.
Yes and no. In the beginning of the manual it says you reshuffle to draw. However under the taking damage part it says that if you take damage on a section that is destroyed you then take damage via cards off the deck that are removed permanently from the game. The note then says if a player cannot draw from the deck because it has been depleated in this way, the game is over. So I would interpret that to say you keep reshuffling until the deck has beem eliminated via damage points.