Go into settings>notifications>scroll down to Words with Friends and make sure your alerts and sounds are set to "ON" If they are already on then try deleting the app and reinstalling it. (You may lose your games in progress though)
Jailbreaking your phone can get you some ringtones or as Crank said there is an app that can make your already songs on your phone into ringers. As far as putting new stuff on itunes will be needed, you can do it with a PC or MAC really doesn't matter.
We have done some parts buying through Amazon before, I would just be sure to purchase within the USA. Though most parts if not all parts are made in China anyways dealing with a seller in the USA is way easier.
I would look on ebay if you are just looking for a screen replacement. Problem is the LCD and the Digitizer(screen) is fused together. When we repair iPhone 4s we usually have to replace the screen and the LCD even if the screen is the only issue.