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Unfortunately if you are proven to be the father the court can order you to pay child support and it can be for up to three years before she filed for suport. So you could already be 3 years behind in payments, but at least you won't be liable for all 13 years of the child's life. You will have to show the court all your earnings and show how many dependents you are supporting so that all that will be considered when the state determines how much your monthly amount should be.
http://www.divorcehq.com/calculators/id_supportcalc.shtml This site will give you an estimate of what the amount may be.
You do not need to pay again.
You should send in the insurance information today so you can meet the Feb 4th deadline. Your employer should not give out any information without your consent or a court order, especially your social security number.
It would be good to contact the mother and try to come to an agreed amount for support. If you can do so, you would draft an agreement that lays out who the mother is, who the father is, what each of you has as income, and what other dependent's you are providing for. Then state the amount of agreed monthly support you will send to the mother by X date each month. Also that you agree to provide insurance, if you can, if not that she will use the support money to provide insurance for the child. If the amount you agree to is reasonalbe she or you or both can file it with the county court in which the child resides and have the court sign the agreement into a final order binding on both of you.
You can also address visitation if you are wanting to have a relationship with this child.