Hello,
I checked your requirements and basically the gameplay will be somewhat like the QuizUp game/app ?
I can add all the features to your app game you mentioned including game center leader-board scores, social sharing of result/score by FB/Twitter, social sharing site logins (if you want users to have a account), in-app purchases.
I can develop the app in Native ObjC so the code will be dynamic and available for future modifications and upgrades to you.
And yes, I can codesign and add developer certificates of your own account to submit the app by your account.
I would be happy to discuss this project in more details with you.
Regards