Am I in a lawful status? Am I just authorized to stay?
Yes, you are in lawful 'pending' status. If you have an EAD you can work. But, travel out of the US w/o a permit isn't allowed.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.
USCIS does not consider pending AOS as "status". You are pending AOS now, that USCIS considers as being in lawful "pending" status, until final adjudication of your AOS. You are definitely authorized to stay and can work with a duly issued EAD.
You can travel out of the country with a valid Advance Parole travel document.
Behar Intl. Counsel 619.234.5962 Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
If you were eligible to file AOS, you should be fine.
This response is general in nature and cannot be construed as legal advice, given that not enough facts are known. Any comments offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship. If you would like additional information based on this response, please contact my office at 510 657 7665 or 415 902 0832 to schedule a consultation.