How do I reinstall my camera app?

You did not delete the Camera app. It's still there. You have it buried in a folder or on another home screen.

Invoke Spotlight Search...http://support.apple.com/kb/ht1430

http://www.padgadget.com/2013/09/23/padgadgets-ipad-tips-how-to-access-spotlight -search-in-ios-7/

...and then just type Camera. It will launch the app for you.

If you still can't find it after that, try restarting your iPad.

http://support.apple.com/kb/ht1430

Not possible. But you should check

Settings

General

Restrictions

Camera

In addition to the advice above, Check: Settings - General - Restrictions - Camera = ???