It's not easy to answer this question, as you don't provide quite enough information. I highly recommend you have a qualified immigration attorney review your case quickly, as the appeal time is very short.
Evidence of a joint mortgage on your home is just one example of the many different things you can use to show that their was a genuine marriage at the beginning. I strongly recommend you contact a qualified immigration attorney to assist you.
The asylum clock measures the amount of time that has passed since you filed your asylum application. It is ascending. Once you have reached the 150 days you can file a form I-765 to obtain a work permit. The form is downloadable, with instructions, from www.uscis.gov
Depending on what problems there may have been in the marriage, she may be eligible to self-petition as an abused spouse. Although this includes mental and emotional abuse, she should contact an immigration attorney as soon as possible as these cases are very fact-specific and require considerable documentation.
You should talk to a local attorney about the possibility of a deferred prosecution. Under this program, if you make restitution, complete some community service and pick up no new charges, the state will dismiss the case and you can have it expunged. Procedures vary somewhat from county to county. Even in a worst case scenario, you are not looking at active time on this unless you mess up on probation.
If your H-1B was cancelled, it no longer exists. There is no such thing as reactivation, I'm afraid. You would need to file for a new H-1B, and the cap has been reached for the 2013-2014 year. There will be no additional H-1Bs available until Oct. 2014, unless the law changes.
I advise all my clients to ignore these letters! Most of the time they are not signed by an attorney licensed in North Carolina, and they rely on people paying out of fear. Never had a client sued yet!
Are you sure you don't mean an MAR (Motion for Appropriate Relief)? If you are not sure how to proceed, you should contact an attorney as soon as possible as there are strict time limits on some of these procedures.