Code 31 is normal. No need to worry about it. If you didn't start the vehicle and drive it (per FSM), I can see it throwing the 14 and 24 codes.
Link to check other sensors:
http://www.xenonz31.com/sensors.html
Running a turbo on low oil can seize it. If the turbo is seized, it will run poorly (with the turbine slowing down airflow and not giving enough air to the engine due to the turbines not spinning). This can damage the engine.
If the turbo is shot, I'd suggest going with the Holset HX35. They are cheap (about 1/2 the price of the Z turbo (both reman)) and will allow for more boost than the stock turbo. Do some research about mating it to the VG30E to learn if that is the route you want to go.