Email / storage back up

Device or computer? Have you tried deleting the account, restarting, and then adding the account back?

OS

Troubleshooting Apple Mail

What does Mail/Window/Connection Doctor Show? If the server is red, select it and look at the Show Details box.

Mail: Mail troubleshooting 

Mail: If you can’t receive messages.    

Mail not sending or receiving messages after updating OS X.      

IOS

Mail - If you can't receive email on your iPhone, iPad, or iPod touch    *

If you forgot the Apple ID (iCloud) password, enter the Apple (iCloud) ID, and click Forgot Password. See if you can get a Rescue or Notification email option. Link to contact Apple Support at the end of the 2nd article.

Apple ID - Manage

Apple ID – Forgot Password  *      

If you have 2 Factor Authentication enabled, if you can't recover the password using the steps above, you will need to use Account Recovery. The Recovery Process is an automated process and the length of time it takes can vary a lot. Apple ID Support can only answer your questions. They can't intervene in or speed up the process. The article below has some suggestions to shorten the time the process takes.

Apple ID - Recover your Apple ID with two-factor authentication account recovery.