IPhone turning off problems?

Just today i found my phone (which i had left earlier) was still on. I have a problem with the top button, it doesn't work, but thats not really my question as i'm getting that repaired later on. It's just that i normally just put my phone down and wait for it to turn off by itself. So what might be causing it and how do i fix it?

How to remove iTunes and USB cord icon on my iPhone 3GS screen?

I had a notification to upgrade my software. I completed the process but, I realized that I made a mistake with my username. Now, my iPhone would not open. It shows an iTunes and USB cord icon on the screen. I have pressed the power button and middle button several times already. Do I need to go back to the application and correct it? Can I still open my iPhone and make it work again?

My iPhone 3GS won't stay on?

So since the weekend my iPhone turns itself off at less than 50% battery, then when I switch it back on again the apple logo appears but it will not go past that before it switches itself off again. The only way I can get it to stay on is if I charge it to 100%
However… Since last night it won't stay fully on even when it is plugged in to the charger in the wall (when I connect the USB to my laptop it is totally unresponsive) it keeps going on and off on its own. It now has 82% battery and will immediately turn off if disconnected from the charger.

Basically I'm wondering if there's anyone out there who can help me?

Added (1). Or you could read the question properly as I said, it keeps switching on and off even when connected to the charger.

Can I buy iPhone 5 without credit card?

I want to buy only 199$ (cash). I don't have credit card yet. I don't wanna pay for the contract either. Because I live in asia and next month I will go there, Can I buy it for 199$ and unlock it in my country? I'm 15 years old. Remember i don't have credit card only cash

Best Anti-Radiation iPhone 4s/iPhone 3GS Case?

My occupation requires a lot of talking on the mobile phone. I just want to know what brand of case is best to prevent radiation. It doesn't matter what the price is, as long as it works. I will need 2 cases, one for the 4s and the other for the 3gs. I've found two cases which are Pong and Snugg. If you could tell me which of the 2 is best or link me to a brand which is even better.

IPhone says it has an email, but there's no no new email

My iPhone 5 shows the little 1 badge on the email app and when I go into it (I have 4 different emails) it shows my work email via Microsoft Exchange as having 1 new email.

But when I go into it there's no new email to be found?

I do not like having the badges on my email nor my phone telling me I have a new email… I check it a lot during the day for work and I will contently be going into it thinking I have a new email and there be nothing.

Anyone had this issue before and how do I remedy this issue?

Added (1). I have tried restarting the device and still nothing.
My last option is to remove my email and add it back (it's work so it's not easy to get back on the phone again).