Most states will allow someone to drive a car regardless of who owns it, so long as they have the owner's permission. In this case, your grandfather is still the legal owner. The fact that you have already insured it in your name substantiates that you have his permission to drive the vehicle.
When driving a vehicle that is not yours, the key is permission. It's much the same as when you are a teen and you're driving your parents vehicle or if you borrow a friend's vehicle. Normally, the owner is responsible for any damage you do to the car. Any damage would fall to the owner, even some tickets would too, depending on the infraction. However, since you have the insurance in your name, you should be perfectly fine. You can always have your grandfather put something in writing, whether it is a text, email or fax (whichever is quickest for you to receive) saying he renders permission and that he is trying to title it over to you.
In the event of being pulled over, the officer has the right to notify the owner of the vehicle that someone else was driving the vehicle. The officer is just verifying you had permission to be driving their car. You just need to explain that you are in the process of changing title and due to additional requirements it is taking a little longer. The fact that you are not the vehicle owner should not result in a ticket.
When you try to title the vehicle it will help if you can get your grandfather to send a copy of the death certificate along with the paper showing he is the Estate Executor. Your grandfather will need to have his signature notarized before sending you the title, though. If his signature isn't notarized you will be back to ground zero.
Verify with your insurance company that they are willing to cover claims since you are not the owner. You do have what they consider "Insurable Interest", meaning the vehicle is technically, although not legally yet, yours. You just want to make sure that there are no loop holes should something happen and you need to use your insurance for coverage. If there are loop holes, have your grandfather insure the vehicle until it is fully in your name. This means he has accepted responsibility and given full permission for you to use the car.
Bottom line is you are fine to drive the car as long as it has 2 things. The vehicle must be insured, as you have already taken care of, and you need permission to drive it. Make your grandfather aware that someone may call to make sure he has permission if anything happens.