How can the admin of a group edit all members default profiles? Is that possible? (Drupal 6 installation)
User Profile Access does not have elaborate access control in the fashion of nodes, so the answer is a custom module that takes over the profile edit page's menu access callback.

Use hook_menu_alter() on user/%user/edit and set 'access callback' to custom_user_edit_access. In that function, run the original access logic to preserve normal behavior, but then add another layer that checks to see if the current user is an administrator in the group and if the active user profile's user is in the group.

For D6, you can either check the user data structure directly, or use the API functions og_is_group_member() and og_is_group_admin().

If you want to special-case the email field to a specific permission once the user has access to the form, that's a case for hook_form_alter() and changing the email field's #access element to use a new permission or an access callback with logic of it's own.