State laws may differ but in general if you are ticketed, in your own name, while driving a friend's vehicle it is your driver's license and record that will be affect, not your friends. It would be different if the vehicle itself was getting the citation for say expired registration.

If your name is on the ticket for running the red light then it is your driving history that will show the moving violation and points, if they are assigned by your state's DMV. If the ticket is in your name, it should not show up on your friend's record and thus not affect her insurance. If you are going to drive her vehicle on a regular basis though your friend may want to check with her insurance provider to make sure you are covered to do so without being placed on her policy.

As for insurance coverage, in many states it is the vehicle that needs to show as being insured when the vehicle is stopped by law enforcement. If you were able to show the vehicle's insurance card that is good enough in many states to show that the vehicle has the state's minimum insurance coverage on it. There are some states though that require every driver be insured, if that is the case then you would likely have been required to show proof of insurance in your name and been ticketed if you could not do so.

Check with your state's Department of Motor Vehicles to see if you as a licensed driver are required to have insurance on you or if it is just the vehicle. If you need to have insurance and do not own a car you may want to look into obtaining a non-owners auto insurance policy.