I'm unable to send mail using my email id as it shows "This Mac can't connect to iCloud because of a problem with 'example@eg.com' ". Please help me.

Please sign out of iCloud in its preference pane, then sign back in and see whether there's any change. No data will be removed from the servers. That said, you should always have a current archiveof the data for safety's sake, even if you don't sign out.

If you use iCloud Keychain, when you sign back in to iCloud follow one of the procedures described in this support article to set it up on an additional device.