I have been working on this for a week and can not figure out what the problem is. I have made sure that all the permissions for user groups are set to "Registered" may edit. Additionally I have set the K2 permissions to "On" for editing. I have assigned all users to this group. However, when logged in, everything appears fine with the K2 articles but there is NO option to add or edit articles. Additionally, the bullets in the Login Module under the avatar are missing "Add" or "Edit" articles.

You can see what I mean by going to inventank.com and login under test/123456 from front end.

There are a couple of issues here.
I logged in but I got an error message from another extension.
It was brief so I didn't have the time to read it.
Also the template you are using does not support Joomla!'s default modal. There are several posts in this forum or you can address this issue to the template's developer.

Finally in the form itself I get two messages. One of a successful login and one of a "Access Denied". Are you using any extensions that enhance/ change Joomla!'s ACL?

I had to go back to a previous version of Joomla 3x and everything you said is now working properly, however, the original issue: UNABLE TO EDIT FRONT END is still not working. There are 2 bullets on the K2 login module that are not displaying right, they are blank. And, there is no option to edit when logged in as the Super User on any of "My Pages". I am nervous to give you the permissions to recreated the issue here since this is public. Please help.

Also the template you are using does not support Joomla!'s default modal. There are several posts in this forum or you can address this issue to the template's developer.

This is the issue. The template you are using is 'hiding' these links. This is a template issue.