I would consult with an immigration attorney to determine whether or not your mother is eligible to apply for an immigrant visa (if she is outside the U.S.). The attorney will advise you as to the process of applying for the visa, check your income to see if you qualify to sponsor your mother (or will need a co-sponsor), give you estimated processing times, and help you gather the supporting documentation needed to file this application. Good luck!
It depends what country you are from. Use this chart online to determine the wait taimes: http://www.travel.state.gov/visa/bulletin/bulletin_5630.html . It is the Visa Bulletin issued by the Department of State. F-2A is the category but each country has different wait times... Good luck.
In order to obtain permanent residency, she would have to be sponsored by an employer or eligible family member as detailed on the uscis web site. A U.S. immigration attorney would be best to go over these options with her.
Travel while out of status COULD (but not always) result in detention by CBP at the airport. I would get your application in the pipeline first. You do not give enough information to determine whether you can even apply affirmatively for residency. A lawyer can review the case for you to be sure. If you do NOT qualify to apply, you could be deported, even though you are married to a U.S. Citizen. Good luck!