Skype and NEW IPAD

your Skype app will ring as your computer based Skype does if someone tries to call you either via your Username and a Video Call or via a Skype number you have setup with your account.

Do bear in mind that is Skype is not the active Application it may not disturb you, depending on the settings you choose in Skype.

Ask a friend to make a Skype call to your Username and see how it rings.

If it is set up in the Notification center to do so, yes. Open the Setting app, select Notifications, find Skype on the list and set the notifications for the app.

In the description for Skype on the iPad App Store, it includes: "Get an Online Number from Skype so people can call you on your iPad." It sounds like you already have the number so you should be good to go.