I have contributors to my website and I want them to be able to click a link at the bottom of the site called "Contributor Login" and once they login I want them to be redirected to the form that they can add new content (items).

Or once they are logged in a new menu item appears at the bottom called "Submit Content" and that link would load the add new item form. However, my problem is that it keeps jumping out into a new page that is a 403 error.

I have the user groups set up to be able to add, edit and publish

Hi. Check again the K2 user group permissions. Note that the user that signs in must be assigned to one of the available K2 user groups with the appropriate permissions.

I have attached my usergroup and a test user that I create with the same permissions that I have for the contributors that I have

How do you expect this to work since you have front-end editing disabled? Enable it and it should work. Also the screenshot with the user is taken from the Joomla! users not the K2 users. User must be assigned to a K2 user group.

To make it more clear, you need to assign the specific user to the group "Contributors".