Verified answer

Right now,

Your dad need to call the credit card company and make you an authorized user on the card. You cannot use it at a store legally if you are not on the account

Your name.

If it's his card his signature has to be on it and also you have no authority to use it. You may use it online with his permission or in a store with your father present. Unless your name is on the card you're not an authorized user and as far as a store knows you could have stolen the card.

Just sign your name.

Sign your own name.