After removing Norton's remnants, I would suggest a reboot and reinstalling avast anew (and reboot again). There are possible additional settings to review after that.
Now, you mentioned Outlook and Windows Mail. One of them should be the default, and avast should recognize it.
About MS Essentials, here you might have some potential conflict with avast, as one of the optional features of it is also an antivirus, that could be in conflict with avast. So try disabling (or even better, uninstalling and removing its remnants) of the antivirus of MS Essentials. The rest of it (like Messenger) should be OK and should work correctly with avast.
Whatever you remove, try the re-installation of avast after a reboot in between, then another reboot and double check the configuration.