EAD
I applied the EAD with I-485 reciept notice in local INS office. I did not bother to apply AP, so I am not sure if I can do that also in local INS.
For me, the officer only takes a copy of I-485 reciept notice and the filled I-765, nothing else. The INS office actually took photos on the spot and asked me to sign on the signature card, 5 minutes later, she put the EAD card in my hand.
The office did mention that it might take a week for background check when we first went in, but she was very nice and called us an hour later at home to come back and pick up the EAD.