It depends on the policy your dad bought. Some say that you can have other drivers (you dad might of had to have to list them on the policy) and some say that you can't allow anyone to drive. one costs more than the other. You can do this with both the full and the liability insurances. Me, I don't have anyone else on my insurance, becuase it's cheaper and there's no reason for anyone to. You need to check with your dad. Life will suck if you are caught driving without insurance, especially if you are in an accident.
Most policies will cover you. Its just like if your dad let one of his friends drive the car. Generally if you have the owners permission, you'll be covered. But if you're a regular driver of the car, he should add you to his policy otherwise you may not have coverage.