The MSE forums are here:
http://social.answers.microsoft.com/Forums/en-US/category/mse
No, Windows Live OneCare must be completely removed from the computer. In fact, the issues you are having might mean that it wasn't completely removed. You should use the cleanup tool -
http://social.microsoft.com/forums/en-US/onecareinstallandactivate/thread/399071e2-49dc-4767-932d-d261e3965943/
You will also need to reinstall MSE after you run it, I believe.
http://www.microsoft.com/security_essentials/resources.aspx
Tune-up and Backup are not available in MSE.
If you used OneCare for backups, you'll still be able to restore from old backups if you use the OneCare Restore tool -
http://social.microsoft.com/Forums/en-US/onecarebackupandrestore/thread/e5d686c8-762b-4b22-bc08-bfb93f911e57,
but you'll need to seek an alternative backup solution.
Tune-up in OneCare simply ran tools already included in Windows. You can find these at Start/All programs/Accessories/System Tools.
-steve
~ Microsoft MVP Windows Live ~ Windows Live OneCare| Live Mesh|MS Security Essentials Forums Moderator ~