You can use an IPad 2 with no carrier at all if you only use the wireless internet with it or wifi. You can use AT&T or you can use Verizon or just wireless internet.
You do not need the internet to use an iPad. However its function will be severaly limited if it does not have access to the internet. Most of the iPad's content is drawn from the internet, either through app downloads or content to its apps or web browsers.You can use the iPad for work such as text input or watching video loaded onto it with a computer along with some apps that do not require an active internet connection.
To use apps you do not need internet, but you do need internet to buy apps.
yes
That's not possible, You can only Use the Internet on Wi-Fi or Wi-Fi and 3G on 3G Models of the iPad.
If you only use your iPad for internet I wouldn't. But if you use it for apps yes, then you can sync your Apple ID.
There are no contracts for an iPad; you can purchase a plan from AT&T for your phone, but for the iPad you do not have to purchase an additional plan when you are going to use the iPad for internet services.
Only is you wish to use it to connect to the internet.
The iPad two if (at the time of writing) the latest generation of iPads, where as the iPad 3G is a iPad one or two that has the ability to use mobile networks to access the internet.
You can use wi-fi on any home internet service provider- for ever! But if you want to use the iPad on the go with 3G, you have to subscribe with AT&T (as of right now).
You can use IPad for gaming, browsing Internet, email management, personal productivity such as photo album, work presentation and entertainment.
Nope You will have to have the internet to download games to the iPad, but most can be played without a internet connection.