An officer has discretion on whether to issue you a notice of infraction (ticket), and if you have more than one violation, the officer can cite you for only one violation if the officer so desires.
A no insurance ticket is a nonmoving violation. If you had insurance but did not have proof on you, you can get the ticket reduced substantially. If you didn't have insurance and get insurance a day or more after you were cited, many courts will still reduce the fine.
No reason for you to be pulled over? You were driving without your lights whether you think it's 5 feet or 5 miles. Once stopped the cop has a right to check driver's license, registration and insurance. If he only wrote you a ticket for the latter that's his choice. Would you have preferred 2 charges instead of te one you got?
If you own the car, you are responsible for ensuring that you maintain continuous insurance coverage on that vehicle. As long as you have a plate from DMV, you must maintain insurance. Only after you surrender the plate can you cancel the insurance.