H4
Monk Monk,
The H4 is valid if your H1 is still valid and you are working for the same employer that sponsored you for the H1. I presume your H1 is valid until 2006, in which case you need not bother about an AP or EAD. You have valid non-immigrant status and so does your wife as long as she is not working and has spouse status.
The only grey area is technically when you have AOS pending, the immigration office expects that you have a parole approval to travel and re-enter. I am not sure if this is held very strongly after the law change that allowed a concurrent filing of I-140, I-485 etc at the same time.
To answer your other question, they do not stamp your AP when you leave the country. They take the I-94 white card if you have one. Other than that, the carrier does not have a clue about anything else. If you have an Indian passport and a ticket to India, everything is good.
AP can be used multiple times to enter and leave if you have multiple entries allowed on your parole. Ginnu makes a good point about getting an AP approved after one leaves the country.
In summary, there is little risk to travel on H1 or H4 that is valid. But you may want to consult a lawyer to ensure that you can travel on H1 or H4 and use it re-enter without a parole. It is still a grey area in my opinion. There is a chance an occasional officer may ask if you have AOS pending and were you paroled.
good luck!
markz
Not trying to be a lawayer......... just to help my fellow immigrant with experience and commen sense. please use your best judgement on any free advice.