How do you know if someone has hacked you ipad?

Game Center is just a place to connect with friends who are participating in group games. There's no way to play a game directly through Game Center. Nor is it more than a very remote possibility that someone has hacked your iPad unless it's been jailbroken. What leads you to think someone has hacked your iPad or accessed any of your games?

Unless someone else has the same game on their own device and signed into Game Center using your same ID and password, it's most likely a glitch in the game. You could contact the game's developer and ask.

As to what jailbreaking is, see:

http://en.wikipedia.org/wiki/IOS_jailbreaking

Regards.