Your question is extremely confusing. Whose car is registered in New York? Whose car lacks insurance? Whose car caused the accident? Who was driving the car? All of that may or may not be relevant. In Florida the person who caused the accident is usually responsible for property damage whether or not he or she has car insurance. It does not matter where the car is registered. In Florida, people go after both the driver and registered owner. The driver caused the accident and the registered owner gave the driver permission to drive the vehicle. Collecting one cent is frequently a different matter.
After an accident, all parties involved with the accident should exchange insurance information. Typically, the insurance companies will talk to each other about repairs and cost.
This depends on the insurance policy. Usually your car is covered, no matter who is driving it. However, if you are driving a car and the owner doesn't have insurance, then your insurance would pay if you got in an accident.
Insurance follows the vehicle, not the driver.
I would call their insurance, if you did not know who they are or they didn't have insurance, I would call your company and they can get the ball rolling.
The insurers of the driver who was deemed to be at fault for the accident.
the car owners insurance The person driving the car would need to submit a claim to their insurance company. There are a few insurance companies that will cover not only the registered owner but anyone driving the car, however this is not usually the case.
She is.
Your insurance will have to pay regardless if the other person has insurance or not. You were at fault.
Absolutely, this person can and will sue you. Just because he/she wasn't licensed doesn't mean that you have the right to get in an accident with him/her. The only thing that will happen to the other person is get a citation for driving without a license, or whatever the case may be. You are still responsible for all damages.
Yes they will, but you may have to pay a deductable if you do not have uninsured motorist coverage, and you you must have comp & coll coverage.
Just because they left, doesn't automatically make them at fault. The insurance company claims department will make the determination base on the facts of the accident itself, not about what happened afterward.