You don't have to show anything while going to India. But while coming back. Keep all the Original three pages of Advance Parole handy for Immigration officer at Port of Entry and make few additional photo copies in case required by Airline.
If you have valid visa stamped on your passport, In that case you don't have to show AP papers to anyone in India.
At POE, Just show the AP papers to Immigration Officer and keep your 485 Receipt and other documents if you have any. In case the officer ask.
Hope this reply your question.