Auto Insurance Claims: 3 car collision not at fault, neck stiffness, fault accidents

Last week I was driving on the highway when traffic ahead came to a stop. I was able to brake and come to a complete stop at least 2 feet behind the car in front of me. The driver of the car behind me was not paying attention and slammed into my bumper at 40 mph, pushing me into the car in front of me. The driver behind me admitted fault, was given a ticket, and her insurance has accepted liability

1) Some friends have told me that the damage to the car in front of me will be paid from my insurance (despite not being at fault), and thus can affect my insurance score and premiums in the future. Is this true?

2) This is the 3rd time in 7 years I have been rear ended, none of them my fault. Will this impact my insurance score? Will it have an affect on my premiums?

3) Even though her insurance is covering all of my damages, should I contact my insurance company to report the accident?

4) My passenger and I had neck stiffness and headaches immediately following the accident, and I stated this in the insurance and police reports. We are both feeling fine 1 week later and the insurance company has offered us each $100 for the injury. Is the acceptable or should we hold out for more in case the injuries appear later? Also, if my credit score/premiums are affected by the accident, could I get a larger settlement to compensate for future increased financial costs?

Thank you!

Hi Lauren,
I'm sorry to learn of your misfortune.  I will answer the questions in the order presented.
1.  The insurance from the car that hit you will pay for the damage to both cars.
Your insurance will not be involved and this accident will have no bearing on your insurance score or rate.
2.  I am not aware of any state where the frequency of non-fault accidents has any bearing on your insurance score or premium.
3.  Most states require that an SR-1 proof of insurance form be filed after any accident.  That form can only be filed by your own insurance company, so you should make a report to them.
4.  If neither of you received any medical treatment, the $100 offer is just to allow the insurance company to close their file.  Without medical treatment related to the accident, there will not be a larger offer and none of this will have any bearing on your credit score or future insurance premiums.
I hope you find this information to be helpful.
Your feedback by rating my answer will be appreciated.
San Francisco Bay Area