You should know that the insurance company is NOT working for you! There job is to settle claims as cheaply as possible, so they will not do you any favors and will try to get you to take the least amount of money they can. You need to realize that personal injury lawyers deal with insurance professionals everyday and know how to present the evidence and argue your case to get you top dollar. By trying to save a buck by doing it yourself, you could cost yourself thousands of dollars.
Normally if you are being sued for property damage then the person that is suing you has to prove there was damage done to the vehicle. If there is no damage maybe they are suing you for some other reason, like lost delivery time or or something. If you have insurance then your insurance company should provide you with a lawyer. Call them. If not call a local lawyer. But take care of this ASAP.
Depends on what the divorce decree says as to who can claim the child. if nothing in divorce decree, I would check with the grandparents and just say you are going to claim him this year on taxes and get something in writing. if both of you claim it will be a big problem at some point down the road. You also might want to talk with your divorce attorney about this.
As the other lawyers stated, most health insurance companies have clauses in their contract of insurance that if you recover the medical bills from a 3rd party that the health insurance has already paid they are entitled to reimbursement. It is better to be up front and find out before hand, because if you have to have a minor settlement hearing with the court, the judge is going to want to know about that. If you don't have an answer it may delay the settlement.
I agree with the other lawyers, there doesn't appear to be one because you cannot tie the shooting into her death. But if you assume there was one then normally only the executor or administrator of the estate can bring the lawsuit.
If you can't pay off the debt then you need to try and work out a payment plan. Sometimes the states have stricter payment plans than the IRS. It might be beneficial for you to discuss this matter with a professional in your area.