Re: "FaceTime app unresponsive: password and Settings issues":
"The FaceTime app also isn’t clickable in settings"
Keeping iPad updated to the newest iPadOS version can often avoid issues:
You can check whether there is an update to install in Settings > General > Software updates.
If iPadOS is already up-to-date, and you still have FaceTime issues:
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First: You might want to check you are correctly signed in to your iPad with the correct Apple Account that you use for FaceTime, Messages, etc.
Sign in to your Apple Account on the web or in your device settings - Apple Support
Eg: says:
"Sign in on your iPad
- Open the Settings app.
- Tap Apple Account at the top of Settings".
If not already correctly signed in:
"Choose a method to sign in:
- Use Another Apple Device (iPad only):
If you have another iPad or iPhone that’s signed in to your Apple Account, bring that device nearby and follow the instructions on both devices to complete sign-in.*
Enter your Apple Account email address or phone number and your password.
If prompted, enter the six-digit verification code sent to your trusted device or phone number to complete sign-in."
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Next: Try Restarting your iPad (deletes temporary files, re-establishes connections, may update recent setting changes etc., and often restores order if something is not working as expected.
If needed: See how to: Restart your iPad - Apple Support
Check whether or not you can now use FaceTime ok.
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if more help is needed:
Apple support provides an article with steps to follow (link below). Steps may help solve the issue.
If you can’t turn on or sign in to iMessage or FaceTime on iPad, Mac, or Apple Vision Pro - Apple Support