If you are intending to sue your bank for mortgage fraud, you should consult with a foreclosure defense attorney who can review the facts of your specific situation to determine 1) if that cause of action exists 2) if there are other claims against your bank.
It sounds like you're the custodial parent based on what you've described. However, it should be stated in your custody agreement who the custodial parent is. Do you have a court approved agreement or is it an informal agreement between you and the father? Most formal agreements require that a parent give the other parent notice before moving, especially if they are moving out of state. Even if there is no court approved agreement in place, the father has a right to object to you moving...
Below is a link to the website with instructions on how to request a replacement green card.
You can file a petition with the court to have custody modified based on the grounds you stated above. In order for the court to modify the order, you will need to submit supporting evidence to show that the current custody arrangement is not in the best interest of the children. I advise that you retain a family law attorney to assist you in filing your request. If you can not afford an attorney, below is a link to the court's website that provides self-help information
There are a few questions that need to be answered such as, did you enter the US legally and has your current visa expired? You should speak with an attorney to get all the necessary information so that they can properly advise you.
There is no debt minimum requirement to file for bankruptcy. However, there are certain requirements to determine if you are ELIGIBLE to file for bankruptcy, such as the Chapter 7 Means Test. In a Chapter 7, you can usually get a discharge in about 4 months. However, in a Chapter 13 it can be between 3 to 5 years based on the Chapter 13 Plan. The filing fees and attorneys vary. If you are considering filing for bankruptcy, you should consult with a bankruptcy attorney to review the specifics...
To determine whether or not you are entitled to spousal support, the court will look at a number of factors such as education, experience and whether one spouse has given up a career to care for children, etc. The court will also take into consideration the number of years the couple was married. In your case, if the majority of factors considered by the court weigh in your favor, you may be able to receive some spousal support for a short period of time until you are able to gain employment.