Firstly, I doubt very much that the low engine oil would cause your issues, however it is imperative that you keep the oil at the correct level.
99% of 350z engine failures are due to low or dirty engine oils.
Although it may not be causing your issues, I would still pull the coils and check for oil ingress, as Paul has said.
I carry in stock the cam cover kit for this problem.
Once you pull your error codes than you may get a better understanding of what is going on.
As has been said, I would not be surprised if it is a cam position sensor.
Keep us posted of any progress that you make.