If I buy an iPhone from the apple store?

Do I just buy the phone itself or do they activate it there or would I have to go to my phone carrier store to get it activated.
I've never bought an iPhone from the apple store so I don't really understand how it all works. I bought my iPhone from the Verizon store and they activated it there. Are they able to activate phones at the apple store to your usual phone carrier wether it be Verizon, sprint, AT&T? Or do you just buy the phone itself and then you'd have to get it activated at your phone carriers store?

IOS7 notification issue

Okay so I just updated to iOS 7 the day it came out and after the first day I noticed that the notification center just stopped working I have no idea why. So I turn off then back on my phone and it works but not for so long once I noticed notifications also stopped coming up on the top I'm getting frustrated so if anyone else is having the same issue le' me know so I know i'm not alone. I also have read an old question with someone with the same issue but with iOS 5.1 I just wanna know if it's a common issue and how to resolve it. (By the way if it means anything I have an iPhone 4S)

What do I do about my iphone?

My iphone 4 got water-damaged a few weeks ago and I just got a call today saying that they won't be able to fix it. I'm locked onto a 3 year contract with fido and I have only had my phone for a year now. What would be the cheapest and easiest way to replace my phone?