Firstly, iCloud does not handle any other email service than its own.
It's in the nature of POP mail that you download the messages from the server, reading them actually on your Mac, as against IMAP mail (which is what iCloud is) where the messages live on the server and are read from there by your devices (like webmail): this is obviously preferable when you have multiple devices.
By default, Mail applications are are usually set up by default to delete messages from a POP server once downloaded, but you can change this in the Preferences so that messages are left on the server for a week, or a month, so that other devices can also download them. However this does mean that you need to remember what you've already replied to, and of course replies will only show on the device or Mac from which they were sent.
POP is an older system, designed in the days when no-one had more than one computer. Some ISPs also provide an IMAP service and if so it would be worth your while to change to that. Failing that, I'm afraid it's live with the limitations of POP or change to another service.