If my rent contract is 11 months (august to june), should I be paying 2 weeks rent for july?

Will you be living there for 2 weeks in July? If so, yes.

If your lease terminates July 30, 2013, then you are not obligated to pay beyond that period unless you are still occupying the unit, or if you have made some other payment arrangement with the landlord.

Why do you think you have to pay beyond the end of the contract? What does your lease say about the termination date and when payments are due?

If you are still confused after you look at your lease, it might be a good idea to contact your landlord -- using a very friendly voice -- and say that you want to be sure you are clear about your obligations so you can meet them... and just ask for clarification about the due date and amount for your final payment.