Can I recover permanently deleted photos and videos on iCloud of a third party

Not possible. Third part sites that say they can are lying. Once you empty the recently deleted folder and if you did not backup another way they are gone forever.

Mike714xxx Said:

"Can I recover permanently deleted photos and videos on iCloud of a third party: Deleted photos and videos on iCloud of a third party ???"

-------

You'd have to go thorough the third party for this, or recover those the olde fashioned way...

 Retrieving eMails:

A. Open Other Folders: Look in the Trash ro Archived folders. See if they reside in there.

B. Check Other Device's Mail App:

• If Mail was enabled on your other devices (i.e. Mac) along with your iPhone computer, then check and see if the Messages app is enabled on it to see if it exists in it. For a Mac, you'd start up your Mac, not connecting to the Internet, and open the Mail app. Then proceed from there with retrieving the eMail messages.
• IMPORTANT: Be certain you do not connect to the Internet while booting up, as syncing would delete it. So, power off your router to avoid the connection. Go here to Learn how to Export it: Import or Export Mailboxes in Mail on Mac - Apple Support