You can remain in the US while your I-485 is pending. You can travel within the US while waiting for the I-485 to be processed if you have a valid passport or a state issued id.
Yes, you can remain in the US. You cannot travel abroad without an advance parole.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.