iPhone 5 Help - Box Swap even WORSE!

Hey, basically I bought an iPhone 5 on contract from 02 a few weeks ago, there was no real problems with the phone other than two simple things:

1) A dot on my phone app was constantly appearing saying I had unread voice mail on the server, however there wasn't actually any there at all, I checked constantly and it said it was empty.

2) Whenever I tried to phone someone, it would take a good 30-60 Seconds until it actually started to ring, and when it finally did and they answered, the phone conversations were practically impossible to manage due to the fact I was unable to make out a word the person was saying as it was like someone was turning the volume of the conversation up and down to the point it was as if they were whispering at certain points. Even if I had apparently perfect 3G signal.

I reported this to 02 who gave me a box swap as they said this was obviously a phone fault.

Surprise surprise, the issues not only remained on the NEW phone, but even MORE issues occured from it.

1) Along with the previous issues, now I was unable to do anything on my phone without 'Please sign into Apple ID' popping up repeatedly, no matter what I did, whether it was sign in or cancel it, it would pop up again and again. Not only this, the Apple ID it was trying to sign me in to was not even mine, it seemed to repeat the ID TWICE, which is extremely weird?

2) I am now unable to also do a lot of things, iCloud will not let me access it, coming up with a sort of error message every time I try. As well as that, I am ALSO unable to send Instagram photos to Twitter as an error message also pops up saying it is unable to connect.

WHAT IS GOING ON?

P.S - I have tried all the common ways to solve issues, such as restarting ect.