Am I required to carry insurance on a vehicle that is charged off but lender will not pick up?

The safest answer for a lawyer to give is yes. But you'll have to use your discernment. Of course, state law dictates at a minimum liability coverage.

As long as it's in your name, you're responsible for any damage caused by the vehicle.

Well certainly if you drive this vehicle, you should carry insurance because it is a criminal offense to drive without insurance. If you are willing to take the risk that the vehicle will be damaged by a falling tree or other catastrophe while sitting in your driveway, then you could can cancel the insurance. But I would not recommend this choice.

Yes, unless you never drive it.

The charge off of the vehicle does not mean very much. But you should do something about getting the vehicle into the hands of the credit tour. If the car is not insured, do not drive it. You might write the creditor and say that into the hands of the credit tour. If the car is not insured, do not drive it. You might write the creditor and say that if they don't pick it up with in some reasonable time, say two weeks, you will charge them for storage, or auction off the car. I am not suggesting you actually do that but rather that you threaten it. If you are in the midst of a bankruptcy, consult your lawyer about the best steps to take.