Read the sticky threads at the top of the Hacking forum here. This forum does not support piracy, so you'll get the legit legal take there.
The chances that your iPad has been hacked are remote, so remote that you should consider all other explanations first. And whatever is going on, no-one can remote control your iPad or computer if you've turned off the internet. The special hidden chip you probably remember reading about was to bypass encryption, not add a super secret wi-fi connection. As far as I know, that got shot down in Congress.
However, the symptoms you are describing while not typical are not unheard of. They are often caused by hidden problems in Settings. You should try things in this order:
Restart: Hold down the power button until the power off slider appears. Slide it off. When the iPad finishes shutting down, hold down the power button again until the Apple logo appears. Apple recommends you restart the iPad at least once a month.
and then a reset if that does not work.
Reset: Hold down the power and home buttons until the Apple logo appears. The iPad will reboot. This usually takes a bit longer than a restart.
Reset All Settings: Found under Settings > General > Reset. This will not erase your content, apps, or accounts; but you will have to re-tweak many of your other settings to get thing where you want them again.
Restore or Go to Apple: If you go to Apple, there is a good chance the first thing they will do (after confirming the problem) is backup and restore the iPad. If you do restore from a backup, and it does not fix things, you'll have to do a clean restore. Problems like this often come back with the restored data.
Before you restore, or go to Apple, make sure all the documents, pictures, and other important files on your iPad are saved elsewhre, either in the cloud or on a computer.