Yes, you should be reimbursed if you were actively insured during that time. I would call the carrier you had and make sure the lien info is listed correctly, and then obtain all declarations and a letter of experience.
Most financing companies will require you to have comprehensive and collision coverage which means you would not be able to get storage insurance. Check with your finance company to see what options you have.
Yes, there are several companies that will insure you without a license. Some companies will require you to get a license within a certain time frame so make sure to find out the details before getting a policy.
Generally, you need to shop for car insurance before financing the car. No matter where you purchase a vehicle, dealerships and buy here pay here car lots will not let you drive off the lot without providing proof of insurance first.
Finance companies usually require you to have insurance on your car while you are making payments. Companies can back charge you for not having insurance - which is essentially called Collateral Protection.