Q: battery

You can try the steps listed in this article to conserve battery power to see if they help: http://www.apple.com/batteries/iphone.html.  If not, sync your phone to create a new backup, import you photos to your computer (see http://support.apple.com/kb/HT4083), and back up your contacts (by syncing them with iCloud or another cloud service or using an app like My Contacts Backup), then take the phone to the Apple store for evaluation and possible replacement.  It should still be under warranty.