Many people facing this Shareplay not working error after the latest iOS updates. I think you should wait for some new updates of iOS 15. I hope in the next updates this Shareplay issue gets resolved.

You can easily fix this Game Centre unable to connect to network issue with the help of these steps: Firstly, Go into settings > iCloud - turn off the "Game Center App". Next, turn on this button Then go to settings > Game Center > logged in. I hope this may resolve your Game Center unable to connect issue.

You should follow this thread. https://developer.apple.com/forums/thread/5464

You can easily fix this email issue easily by checking your email address & entering the correct details. If it doesn't solve your issue you should try to set up your Apple Mail account again. You can read more about it here: https://support.apple.com/en-us/HT201419

There may be a chance of your email address error. You should contact again to Apple support team. As you have already tried to contact the support team. You should try to connect with some Apple professionals.

We all need a backup of our important files for different purposes. But sometimes we all face difficulty to archive the backup of iTunes. However, You can go & visit this to locate your backup files: https://support.apple.com/en-us/HT204215