I have multiple users for one organization. How can I have one of those user accounts be a main/master account that can view all open and resolved tickets for that organization?
You can do this with the Deskpro organization managers feature. You can make a user a manager from the agent interface, either in the organization record or the user's record. See the agent manual for details.
Organization managers can see all their organization's tickets by logging into the portal, and they can also choose to automatically join all the tickets as a CC'd user from the portal Edit your profile page.