I'd like to know a proper way to add Machine Groups under a single Organization. Also, I'd like to know how the .root Machine Group gets added.
The proper way to add machine groups to any Org would be via System > Manage. You'd have to select the Org in question and from there navigate to the Machine Groups tab and add a new one by clicking the New button.
Every time you create a new Organization, the default Machine Group that gets created is: NewOrganizationName.root. You can delete a .root Machine Group, as long as it is not set as the default one.