She is already out of status. The best thing at the moment will be for her to return back. Filing an extension at this point is not possible.

Note that if USCIS approves the extension, it will be limited to 11/8/2022, the time that you requested. Your mom was supposed to leave the country...

If you already filed separately then wait for an RFE.

The best thing to do will be contact the specific consulate you plan on visiting to see if you are still eligible.

This could have been avoided. Re-file the whole package with proper support I-864 documentation. Hire an attorney.

Visa overstays generally will be cured by a bona-fide marriage to a U.S. citizen. That being said, be mindful of other issues that may come up such...

Green card comes with requirement of residing permanently in U.S. Otherwise, you will risk losing it.

It is not a good idea to travel if you are not on a project since you maybe asked by CBP regarding your employment.

You wont be able to work on F2. However, there are some other visa types that will allow you to work provided you are eligible.

You can re-enter the U.S. in F-1 status before the start date or after the start date of your EAD card. Make sure you have a 'travel I-20' before...