Help me to implement this plan - limit users to edit content
I would look into the Node Access User Reference module as well as a lot of the other content/node access modules out there, eg, this list off drupal.org.  After getting a good grasp there, it would be up to you to code up the integration of permissions unique to your site, but basically you would need to alter the node forms for this content type, check in there if a user reference is NOT yet set, and if so, set it to user editing the content and then be on your way.