I have a new car which was purchased in New York. It is registered in New Jersey and has New Jersey plates. May I go to an inspection station show my documentation and get an inspection sticker?

Yes, as long as you have your NJ address and paperwork you'll be fine. Great location

Proof of insurance a valid NJ DRIVERS LICENSE and NJ REGISTRATION then you can get the inspection. But make sure you have no check engine light on and all lights are working if anything is not working you will fail

If you currently have New Jersey plates, you can certainly visit the NJ Inspection site.

I am not sure

Assuming you can also show that you have proof of insurance, yes.