How to restore my iphone without erasing my media and data?

I updated my iphone from ios 5.1 to ios 6.1.3. After it got done, the phone made the indication to be connected to itunes. After connecting to itunes it said "iTunes has detected an iPhone in recovery mode. You must restore this iphone before it can be used with iTunes". And by restoring i know it will erase all my media and data saved on the phone. How can i prevent this?

How to get pictures from my broken iphone?

I had an old Iphone that fell in the water and doesn't turn on. I got a new iphone now but I want the photos from my old one. Is it possible to get those images somehow?
Also, I still have my old phone.

Why does my IPhone light up?

Around every 10-30 seconds my IPhone 4 automatically lights up (when in lock mode). I believe it is doing it whenever my 3G service (AT&T) changes its signal… I.e. Goes from 4 bars to 3. But i'm not sure if that's the problem. It is really killing my battery horrifically and i would really like help. Is there a setting to stop this or does anyone know how to solve it?

Is 1GB of data be enough for an iphone 5?

Tbh i have no clue what a gb is, but will 1gb be enough for an iphone 5? I'm a teenager so i will probably be on social media websites like twitter etc quiet alot and will take a fair amount of pictures and use a fair amount of apps.
I have Wi-Fi at home so i'll be connected to that whenever possible which will be most of the time, so will it still use up the data when i'm on the internet?
cheers.

My iphone 5 is acting weird

So my iphone five shut down by itself with full battery and kept starting up, but the apple logo would fade away and my phone would shut down and do it over again for about 10 minutes. I took it to AT&T and they said if it keeps happening to take it back to the apple store. It hadn't happenned for almost another 4 months, but just today it would shut down, restart about ten times, it went to white screen, then it turned on, but had a white frame around the edges of the screen, the shut down and started resetting again. I wasn't able to use it for hours, until it finally started working, but i'm positive it will happen again. Do you know what's wrong with it?