To clarify about editing comments, I don't think you're saying that the author of an anonymous comment should be able to edit it, correct? That would be problematic, since there would be no safe way of making sure that the editor is the same as the author because of anonymity. The only thing that can be verified is the IP address, which is not a reliable indication of identity.
Instead, what we're discussing is the ability of a logged in user to edit an anonymous comment. That can be done by moderators. The reason I said "optionally" is that by default, moderators are able to delete comments but not edit them. If you want a moderator to be able to edit comments as well, you need to set:
$wgGroupPermissions['csmoderator']['cs-moderator-edit'] = true;
Setting up arbitrary groups (other than moderators) who could edit each other's comments would be difficult to implement.
There is indeed already an edit history on all comments, since comments themselves are stored on wiki pages. The interface is currently not too elegant, since you'd need to find and navigate to the comment's page, but the information is available. If that becomes a high priority feature request, an easier way to view comment history could potentially be developed on top of the already existing retained history.
So, in summary, I will try to find the time to add the ability to post anonymous comments. All other features (the ability of moderators to edit and delete anonymous comments and viewing comment history) should work without change.
Thank you for helping me to think through the design of this feature.