No matter what I do, my wall posts always show as "Not Published." I want to allow users to post to their own wall, but it doesn't seem to allow this.

This is configured on a user by user basis. They need to edit their profile and set posts to be auto-published for the wall tab. User can post on their own WALL, but can not post on their own GUESTBOOK; please ensure you're reviewing the correct tab as there are 3 (Guestbook, Wall, Blog).

Also, I would very much like to disable the profile owner's ability to delete ratings. Is there any way to do this? I want members to be able to rate other members, but do not want them to be able to remove negative ratings. This may be something I need to post as a feature request, as I do want moderators to be able to modify or remove comments.

Best I can suggest for this is to install rating fieldtype plugin and have a separate field for rating a users profile. Otherwise you'd need to edit the guestbook tab via the profilebook PHP files and remove the delete feature except for moderators (would need to do an isModerator check on myId).