Should I be able to change the Author of an Article in the Backend. I have a regular user in a user group and his name doesn't show up in the Author list.

What I am looking to do is created an Item in the back end for a site user, so that he can only modify that item without having the rights to add new items. My problem is that in the Author list it only shows my Name and none of the users from my site.

This is a big problem. Because only admins show up in the backend author list, if you edit an item from the backend, then the assigned author changes to the admin at the top of the dropdown list.

This effectively prevents backend editing.

You have to assign the user as an Author or Editor in the Joomla! User Manager, not the K2 User manager..