How can I see if my ipad 3 has been hacked?
There isn't a practical way for your iPad to be hacked and/or for the system to be moved into, at least without physical access or a jailbreak running. 

They could, however, get your Apple ID password if it's not particularly strong or if you reuse the same password on multiple websites, and that can give them access to backups, your calendar, location via Find my iDevice, among other things. If you secure your Apple ID and you haven't jailbroken, then you'll be just fine.

It's highly unlikely that you'll ever have your system accessed because of Apple's review process for apps and the sandboxing requirements imposed on them.