I got my permit in December 30th 2013 and I have to hold my permit for 9 months before I get my PDL , how do I know I have had my permit for 9 months, do I count the month I got it, can someone tell me how many months I have.

do I have to wait exactly 9 months ,because people told me I didn't.
after I did 60 hours and Drivers education

You have two types of insurance coverage. Collision and Liability.

Your liability coverage is what pays for the other guys damage. There is no deductible.

Collision coverage pays for damage to your car. There is a deductible for collision.

So in your case Liabilty is what is paying not Collision. You will have no deductible.

How long does it take to track a license plate number?

My neighbor while driving her mothers car, ended up hitting another car. From what I saw it wasn't bad, only my friends car had it's mirror flipped back. I'm wondering how long it'll take for a letter to arrive stating the accident, if the other party decided to call the cops and they got her license plate number. It;s the first time I'm involved in an accident, and I'm wondering if im going to be involved in this, even if I was only a passenger.