How to sync messages and email on multiple devices: phone, iPad and desktop Mac?

Messages in iCloud will sync your devices: https://support.apple.com/en-us/HT208532

Your email accounts simply need to be set up on your devices. https://support.apple.com/en-us/HT201320

Mail sync is not working I have three main iOS devices and a desktop if I delete mail on the desktop which is running the latest greatest whatever it is, I have to still delete the same email on the iOS device. That doesn’t seem right.

You might want to start your own post. A new post would be much more visible. Are the email accounts IMAP accounts? Are you allowing time for the deletion to sync?