It normal with POP3
When download mails from POP3 remember that you can say "delete messege from server" and this in common on desktop/laptop devices that it's on as standard because your POP3 provider properly only give you XX MB storage (in the old days it was 10MB today it's someting like 2GB)
But on hand held devices it's common that it do not delete the message from the server because that it's most common that you also want you mail on your desktop/laptop
Why it's marked as unread both times is because POP3 do not support the idea of storing mails on the server, so it do not support the read/forwarded/replied tags.
if you switch to using IMAP then the mails are stored on the server (and you can tell your mail program to store a copy for offline use)
Then all tag, draft messages or folders and so on will be stored on the server.
and there will not be any difference if you use your phone, laptop, desktop or web mail to view you mails