If your vehicle get stolen and the auto insurance pays the blue book value would the gap insurance cover the rest of the payment on your car loan and what is the limit?

When a car is under lien and stolen/wrecked, the first payee is ALWAYS the lienholder. You will receive nothing, and the lienholder gets reimbursed for the value of the car. Any outstanding would be your debt. Most insurers make deals with Lienholders to indemnify and settle up the loan. Not always though. MAKE sure to ask the Insurance company how much was paid to lienholder, and ask for proof too!