One of my COX.NET email accounts disappeared from my Apple laptop

One of my two COX.NET accounts disappeared from my Apple laptop that I use often. It is still visible and useable on my other laptop, my desktop and my iPhone.  I tried to add it back on the laptop, but I get the message "this account already exists".  (It shows up on 3 of my 4 Apple devices.)  I have two COX email accounts, and the one that is still visible on the laptop, has an iMAP setting. The missing account is a POP.  I also maintain an iCloud email account, which works flawlessly and syncs to all devices.

Questions:

So, how do I get this email account to show back up again on my one laptop?

Do I need to change the missing account to an iMAP acct?

If I do that, will my all saved mails in the missing account be retained?

Will this also allow my four devices to be synced with each other?   

Thanks for any help!