If you file, you pay. Call the divorce department clerk to see what forms of payment they accept. Few or none will accept a personal check, so you will need a bank check, money order, or in most courts you can pay with a debit or credit card in-person at the court. Good luck!
When a party has breached a clear and unequivocal court order - such as a Judgment of Divorce - the other party can file a Complaint for Contempt. There are some defenses that he may have, which you will need to discuss with an attorney. You may also be able to seek attorney's fees. Good luck!
Call the divorce department at the Probate and Family Court to ask how your particular judge handles this matter. The clerk or judge's secretary may have some insight. Also there are some exceptions to taking the "mandatory" class so ask the clerk when you call. Good luck.
You really need to speak to an immigration attorney about this. You can call the Mass. Bar Association for a referral to a reduced-fee attorney (if you qualify) or a local legal services association for pro bono representation (again, if you qualify).
Sorry for your loss. Unfortunately, there is no definitive answer. It could be used as a negotiation tool depending on other facts of your case. You should see a lawyer to go over the divorce statute and various options. Also make sure you disclose the matter on your Financial Statement.
As long as your sister isn't looking to live in the house post-divorce, then it might be in her bets interests to leave. She should speak with an attorney about the pros and cons of being the party to vacate.