Bad unit.
If your pictures are blur and you hear noise from the camera it's because it has a "hard time" focusing.
Take it to Apple, you will receive a replacement.
And about the bad battery life : It's a new phone, you use it with every occasion (i.e. some people check the time on it even if they have a watch). Also, it has iOS 7 which is not very optimized. Yet.
Bad battery life is typically a problematic app. If you restored from a backup onto your new phone that is most likely the issue. You can try to simply reboot (restart) your phone but you may end up needing to restore from the same backup again or restore the phone as new and manually put your apps back on it.
I'm not the search police, I just don't have any links when I say do a quick search for battery and you'll get a ton of threads with various tips and tricks. You may find that it's just a matter of low signal strength.
I have a lightning cable hooked up to my Sony SMART TV and a dock so when I put the phone in the dock it charges from the TV ; it takes about 2-3 hours for a full charge.
If I charge it form my Macbook Pro it takes 1:30 hrs.