Should I downgrade from iOS 6.1.3 to 6.1.2? Because some apps won't open. It keeps on crashing.
Tap tap, GarageBand, and other apps won't open. Is it about the firmware?
iPad 2, iOS 6.1.3
You cannot downgrade the iOS since it is not supported. This support article explains how to trouble shoot 3rd party apps on the iPad.
http://support.apple.com/kb/ts1702
If all third party apps will not open, try downloading another app. Any free app will work or any already purchased app that is not currently on the iPad.
If the troubleshooting article doesn help, I would try this. Close all apps and reboot the iPad.
Tap the home button once. Then tap the home button twice and the recents tray will appear at the bottom of the screen. Tap and hold down on any app icon until it begins to wiggle. Tap the minus ➖ sign in the upper left corner of the app that you want to close. Tap the home button twice.
Reboot the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider if it appears on the screen - let go of the buttons. Let the iPad start up.