Your son just needs to report it to his own insurance company and give that information to the adjuster who is calling. The fact they exchanged numbers shows that it was not a hit and run. The other company does not care so long as your son's insurance pays for the repairs.
Legally there is nothing blocking the claim. As a practical matter you have a weak case. With minimal property damage and a two month delay in getting medical care, it is a long shot as to getting a verdict in your favor and unlikely that you will get a settlement offer. You already have a lawyer and they should telling you this. Tread carefully in racking up medical bills if you have to pay them regardless of case outcome.
It sounds like you had some liability coverage but the uninsured carrier is pursuing you for what they paid out over and above. You have a lawyer still, so have them keep fighting liability on the case. The reality is, even if you "lose", they can put a lien on the house but they would not want to foreclose on it as they would have to pay off the mortgage and there would be nothing leftover anyway. Being broke makes you somewhat judgment proof. Bankruptcy is an option if you lose the injury end...
There is no law in play but they will likely call bs on you because it is very suspicious unless the damage was well detailed in the police report or you have photos at the scene that support the allegation. Coming along 6 months later out of the blue will likely draw a denial. Nothing to lose though so tally up whatever proof you can and give it a try.
The correct inquiry is to explore your options with your international insurance. If the at fault insurance is refusing to pay, then you may be able to get them to turn the benefits on. Dig deeper on this issue. Liens can be helpful as a last resort, but make sure you know how much insurance the driver has and how much available underinsured motorist insurance there is. If the surgery is going to eat up too much of the available coverage, don't do it.
No, it has to go through the probate court and none of the money can go to you, even though you lostoney taking care of him. Be sure to check and see if there is any excess or underinsured insurance available for the claim though before settling.
Wages and punitive damages are taxable, injury compensation is not. If you try your case to verdict, you will get taxed on the appropriate part. If you settle, a good lawyer will see that it's not taxable. If you are paying the full 40% in fees for litigation, you are getting your money's worth because the presuit offers must have been low. The attorney fees are the reason you have the offer at all. It's not easy getting good value for clients.