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Previously I have read that to have your own ship you must be an officer. Does this mean that I cannot have a small ship for just my character to fly around the planets in?
That would be up for questioning. You might be able to posses a small shuttle, Wim Herzog for example originaly had a ship before it was ret-conned out of existance. You would probably have to ask Wes or Yangfan, since they will likely make a decision based on your characters background.