Q: unread exchange email messages  that do not appear on device

If it's an exchange account, that has nothing to do with iCloud or your iCloud email account.  You may need to delete, then re-create the exchange account on your device.  You may also want to try to force closing the mail app (from the home screen, double-tap the home button, locate Mail in the list at the bottom, tap and hold it until it wiggles, tap to close it, tap the home button again).