You only need identification for airline travel not status. However, you do put yourself at more risk. As well and depending on the length of time you've overstayed and your family's immigration history, you may want to rethink your situation with the help of an experienced lawyer.
Yes, so long as the traveler has government issued identification (e.g. driver's license, state identification card, passport).
While this answer is provided by a Florida Bar Certified Expert in Immigration and Nationality Law, it is for general information purposes only and an attorney/client relationship is neither intended nor created. You should seek out qualified counsel to review your case and provide you with advice specific to your situation.
Not without risk.
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.
I agree that you can travel within the U.S., all you need is to show your passport - airline and security personnel are only/mainly checking if your name matches that which appears on your ticket. While you do expose yourself to some risk, the risk is much greater when an alien drives a vehicle without a license.