Should I give a statement to the insurance company of the driver that hit me after I’ve been struck by a car?

No. The insurance company for the driver who hit you is trying to protect their driver, find a reason to blame you for the accident, and limit the amount of money they may have to pay you for your injuries. You should speak to a lawyer before giving any statement to an insurance company for the party responsible for the accident. If an insurance adjuster calls you, get the claim number and the phone number for the insurance agent and pass that information along to your lawyer.