My iPhone 5 keeps on freezing and shutting down

Hi guys.

Around the end of April we decided to get an iPhone 5 from dialaphone.com. The phone was totally fine until about last week, when it started to lag and then, after a few minutes after being switched on, black out. We have tried to restore it using iTunes many times, but there was either two outcomes- it either has the same problem as before or has a continuous booting logo (on for five seconds, then off for five seconds, then on for five seconds, and so on.) Something notable is that instead of turning off, it had a completely blue screen. Also, there was another problem that developed after. If you successfully tried to turn the phone on, the amount of battery left in the phone would be stuck at that level, e.g if you turn it on and the battery in the corner says 66% when you turn it on, the phone's battery indicator would be totally stuck 66% even though the battery is draining.

We have taken it to many places, including EE (the carrier of the phone). We are planning an appointment for a Genius to look at it today. Somebody told me that the "software deleted itself", others say that the phone is overheating because of the very hot weather. If somebody could give us a mere suggestion, it would help ALOT.

Thanks,

Marcus