The show edit buttons on the repeater only work from the admin site. You might be able to customize this if you clone the webpart and make your changes.
An option is to use the user contribution webpart, but that would require your repeater to link to a page that has that webpart on it.
You could create a custom webpart based off the unigrid. This article might help on how to do it, or the documentation.
Another option would be to do it custom, maybe using ajax calls to update the pages.