The lock symbol means that screen rotation is locked. That has nothing to do with the mail app. You can unlock the screen rotation one of two ways depending on how the side switch is configured in the general settings of your iPad.
Try the side switch above the volume rocker first and see if that unlocks the screen. If that doesn't do it, double tap the home button and swipe to the right and look for the lock icon all the way to the left.
If the screen is unlocked but still will not rotate, reset the iPad.
Reset 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 - let go of the button.
As for the mail being frozen, if you tried the reboot... See if that unfroze the mail app. If it didn't try this. Close the mail app in the recents tray, then reboot the iPad.
Tap the home button to go to the home screen, if you are not already on the home screen. Double tap the home button and the recents tray will appear with all of your recent apps displayed at the bottom. Tap and hold down on any app icon until it begins to wiggle. Tap the minus ➖ sign in the upper left corner of mail app icon. Tap the home button. Then reboot the iPad like I described above.
If you want to read about how the side switch works, take a look at this.
http://support.apple.com/kb/ht4085