A: Assuming that D.C. has the same statute of limitations as Washington (3 years) it would appear that it is outside the SOL. But most jurisdictions have rules that allow someone to file suit within the statute and have a grace period to find and serve the other party. From what you've provided, I can't say for sure, but that would be my suspicion.
In either event, let your insurance company know. They will have a duty to defend you in the lawsuit, and they will explore whether the lawsuit is barred.
A: Your options depend on how the other person tries to charge you a ridiculous amount. If he or she is just calling you insisting that you pay them, you can pretty much ignore them for the time being.
If they attempt to sue you, you will need to do more. It also will depend on what they are suing you for. It is not uncommon for a person to be injured in a vehicle that does not show a lot of damage. It is also difficult to contest the amount of someone's injuries without an attorney and hired experts. If they are claiming personal injuries as a result of the crash, you will probably do better if you hire an attorney to help you. If you had insurance at the time, one of the benefits is that they will defend you at no additional cost.
If they are trying to collect money for the car that you say was not damaged, then they might be pursuing this in small claims court. The good news for you is that they won't have a lawyer in small claims court either. Keep in mind the things that they will have to prove to be successful, and focus on how you can disprove any of their claims. The first thing they have to prove is that you were at fault for the accident. Your question indicates that you were not at fault. If that's the case, then it doesn't matter what kind of damages they are claiming, they can't get them from someone who wasn't at fault. Your best outcome in all of this comes from winning a fault determination.
If you are found at fault, the next best thing you can do is decrease the amount you are on the hook for. If they claim bigger property damage than occurred, take your witness with you to testify about what their car looked like. If your car has not had any work done on it, take pictures of your car to show that any alleged damage doesn't match up with your car.