Each organization has many members, You can add your members in your organization and then add them to any project easily and without need of e-mail.
Adding members to organization doesn't mean that they have access to all the projects inside that organization. You should add each member to projects. You don't need to enter their email address after you've added them to organization.
Please notice that if you delete an organization, all the projects you have inside it will turn to personal projects.
For removing a project from an organization you can go to "Project Settings" and change the organization to "Personal".
If your organization has more than 10 members, you need to Upgrade Organization to Business Plan.