Goto task menu, select craft and then alter the task details to see what you can craft.
The ship always falls. Everyone can cure injuries, but that might hurt. A mechanic is a good choice to fill the second seat when inspecting the rover. Injuries cannot be prevented.
The puzzle part is to figure out what to do. The strategy part is to optimize the order of what you do. Finishing the game is not the only challenge as you might see later. Good luck :-)