You should hire a PI attorney who would review the case with you and see that you get the best outcome available. What will you do if you later realize that you will have to sue the other driver because their insurance company is being unreasonable with their offer?
I agree with my colleagues. If your mother entered the US eith a valid visa and overstayed then possibly a green catd if she meets other req. Once she gets green card she is eligible for naturalization after 5 years.
You should have contacted the police. If her insurance company determines that the accident was her fault then her insurance company will need to pay you to repair your car damage, to pay for any medical treatments you received as a result of this accident, and any pain and suffering. You should consult with an a personal injury attorney for a free consultation.
There are too many unknowns to your questions. The best thing to do is to speak with a personal injury attorney who could help your brother navigate through these and other questions to determine the best course of action. RCW 46.61.145 governs rear end collisions. Furthermore, in the event the other driver doesn't have insurance, if your brother has UM/UIM coverage, it would be covered under that coverage.
Did your health insurance company pay for your medical expenses? If you answered, "yes," your health insurance has right to be reimbursed. You should speak with a personal injury attorney who could review your case and go over your options in details.