Since the ship only supports two crew members, does it mean we are limited to a pilot and a doctor as crew (it would be helpful if the crew positions/roles could be fleshed out more for us)?

We don't see the roles being as strict as just 'pilot and doctor' and envisage both players taking part in recovery and treatment. While landed or docked in space, both crew can safely help. However, there is nothing to stop the pilot leaving their seat to help while the ship is flying (ideally in safe space!).