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.
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.