1 Stop emailing him every day. It's not professional. If he doesn't respond right away, wait. People are busy and may not have time to answer you right away.
2. If he doesn't get back to you by the third, move along. A client that ignores you for over a week isn't likely to pay you on time either.
He can't leave you any feedback if he doesn't pay you, so don't worry about that. The contract might remain open but it's not going to hurt you. Just let it be for a while and if you don't hear back email him and ask him to close it. If he doesn't you can just end the contract yourself.
Also the deadline is usually a guess for many clients so it isn't going to look bad on you, especially if you don't have any info from the client.