Q. What documents do I need to enter US on EAD/AP?
A. You will need only your passport and EAD/AP combo card. Some people also carry (but not necessary) I-485 receipt, I-797 approval form (H1B) and letter of employment from your employer.
Q. What is the typical scenario at the airport when entering US?
A. Here is a TYPICAL scenario (experiences may vary):
Once the flight lands, head over to the immigration line. Since you have EAD/AP, select the "non-immigration" line. People with GC/US Citizen can select the "US Citizen" line. Once you are with an immigration officer, give them your EAD/AP combo card and your passport. They will scan your fingers, take your photo and may ask few questions (such as where you are working, how long was your vacation, what was the purpose of your vacation, etc). Once that is complete, you will be directed to a secondary inspection area.
Over there, you will be greeted by another immigration officer and you will be asked to put all your immigration documents in a container and asked to wait. The wait can be anywhere from 10 minutes to 2 hours (depending on how many people are waiting there). Once the check is complete, they will give back your immigration document and I-94 with Paroled status in it. The I-94 validity is around one year. Make sure the I-94 dates are correct. Once everything is complete, you can leave the airport.
Q. What is the purpose of secondary inspection?
A. The purpose of secondary inspection is to make sure that your adjustment of status (I485) application has not been rejected.
Q. What is the immigration status once a person enters on AP?
A. The immigration status is "Paroled" in to US. Your previous immigration status (H1, etc) is no longer applicable.
Q. Once a person is "paroled in" to US, does the H1 becomes invalid?
A. Many lawyers are conflicted on this. According to some lawyers, H1 is no longer valid once you are paroled in (which means if I485 status is rejected, the person status would be out of status). Some lawyers say that if H1 is with same employer who filed I485, then it is fine (under the Cronin memo). The employee only needs to file an amended H1 application. As always, talk to your company lawyer about this.
Q. What is the status written on the I-94 card?
A. This depends on the officer. Some may write (a) AOS (for adjustment of status) or (b) D/A (for district authority which means paroled) or (c) Paroled until ... (date)
Q. Do I need to submit my old I-94 card before leaving US?
A. It is not required to submit your old I-94. It is recommended by few people to submit it to ensure a seamless transition when you later on enter US in a new status (parolee).
Q. Should I enter US using AP or should I go for H1 stamping?
A. This depends on individual basis. H1 stamping can be a hassle due to Jan 2010 USCIS memo about establishing employer-employee relationship. If you want to skip this hassle, you certainly have an option to enter US using AP instead of H1.
Since each persons has a different case, talk to your company lawyers about the pros and cons of using AP or H1.