I would definitely refile the I-601A and submit the evidence of the postpartum depression. Without an approved waiver then your husband will have to remain outside of the U.S. for 10 years. There is no limit as to how many times you can submit a hardship waiver but you will have to repay the filing fee. I wish you the best of luck!
You will need to consult the latest visa bulletin for your priority date at http://travel.state.gov/visa/bulletin/bulletin_1360.html. Once your date is current then you will pay the required visa fees, complete the DS-260, I-864 and submit the additional required documents.
When you are applying for adjustment of status (green card) there is no extra fee for the EAD so you should apply. Of course once your husband becomes a lawful permanent resident he does have legal permission to work in the U.S.
There is no statute of limitation as far as filing for a U Visa. However, not all crimes are eligible for U Visa relief. Also you must demonstrate that you have suffered substantial physical or mental abuse as a result of being a victim of a qualifying criminal activity.
I have attached a link which outlines examples of qualifying criminal activities.
If the National Visa Center has received all of the necessary documents for your case then you should expect an appointment by the end of December or January. Currently all of the appointments have been filled for November. Good Luck!
Your friend may be eligible for Cancellation of Removal if he can show 1) that he has continuously resided in the U.S. for at least 10 years; 2) he has been a person of good moral character throughout this time; and 3) that his removal would result in exceptional and extremely unusual hardship to his U.S. children. In addition, there are certain crimes that would make him ineligible for filing for this relief. He will definitely need to seek counsel to represent him with his case. There are...
Based only on the information provided, your mom can file form I-130 to petition for resident status. According to the November Visa Bulletin the priority date is October 15, 1992 for children (over 21) of lawful permanent residents. This means that you will have a long wait ahead of you.