Why won't Facetime ring when somebody calls me?
Go to ‘Settings’, then to ‘Do Not Disturb’ and make sure it is set to allow all calls from FaceTime.

Go to ‘Settings’, then ‘Sounds’, and make sure you have a ringtone for calls / FaceTime set.

Finally, make sure your iPad is not in Mute mode by swiping from bottom of the screen upwards and tapping the ‘Bell’ icon to disable it (or, if you have an older device, and you have ‘Mute’ set under ‘General / Use side switch to...’, switch the side switch on). Having Mute mode enabled will prevent the device making any sound when called.