"Can I apply for advance parole after I have received my EAD (Employment Authorization Document) and social security card? I didn't include that when I applied for my pending adjustment of status, I later realized that I might want to travel but that may happen before my green card has been issued. Are there any dangers for that on my AOS?"
You can always apply for the advance parole. If you had applied with the adjustment of status, there was no fee. Yes you can apply, but it isn't free. We also recommend not leaving the country until you have it. Avoid that nightmare.
Our advice, based on so many stories we've heard, is just try not to travel until you get your green card. Of course, if you have to, like for a medical emergency or something, you must do what you need to do. But it's highly recommended to avoid travel for simple vacations or non-urgent trips. There's a chance you could be detained at a port of entry for hours or even days without your green card.
