Why aren't my applications and iMessage working after downloading iOS 7?

I have an iphone 4s and I recently downloaded iOS 7 and since I have I have had a few problems with my apps and iMessage. When I click on an app it will say ‘Connect to iTunes to Use Push Notifications, “___” notifications may include alerts, sounds and icon badges.’ when I press ok it will go away however when I try to open Snapchat the message will come up, i’ll press ok and it will keep reappearing every second and I am unable to use it. I have tried deleting snapchat and then reinstalling it, turning my phone off and then back on and it is still not fixed. I’ve also connected my iPhone to my laptop, with the latest version of iTunes downloaded and synced it and it’s still not working.

Also, I tried to set up my iMessage my password is definitely correct because I have tried it lots of times slowly and it still keeps saying ‘iMessage Activation, Could not sign in. Please check your network connection and try again’ my network connection is full bars and it still won’t work.