The Tarellian ship was first seen in the TNG Episode 'Haven' and all our information comes from that episode. We know from Geordi that these ships are usually warp capable. It is also seen to have a transporter system. I have tried to explain the very unusual appearance of the ship by theorizing that the 'Glowing Ball' at it's heart is a massive fusion reactor. The part about the resilience of the ships stems from the fact it had been 'missing' for over eight years and given the reaction these people seem to evoke, they where very unlikely to have had much in the way of assistance during this time.