While it can vary by the individual policy procedures of your lender, they should be able to backdate those charges if you're able to show proof of insurance for the duration of the loan. You can request a policy declaration or binder from your insurance company which will show the date of policy inception.
While it can vary by car insurance company and individual agents, some may probe when doing quotes to see the status of the vehicle to make sure you are getting the correct policy type and the correct coverage. If you have a loan or lease on the vehicle, you're more than likely required to carry gap and collision and comprehensive coverage.
Gap insurance is designed to work with your comprehensiveand collisioncoverage, not as a substitute. Basically, gap insurance will kick in if you total your vehicle and the amount you paid out by your insurance company isn't enough to cover the value of the loan.
If you have a leased vehicle, you're technically renting it and thus must maintain comprehensive, collision, and probably gap insurance. Although it might be more expensive to get these coverages, it will save you much more money in the event of an accident.