If your question is primarily about how to allow the user to edit a form (as the title suggests), then I think the way to go is
- Create a new role at /admin/people/permissions/roles and call is something like 'editor'.
- Then go into the permissions page at /admin/people/permissions and give the new role 'Edit any content' permissions under the 'Node' section for each of the content types you have.
If you're simply wondering whether all those content types are OK, I'd say that having 10 content types for a Drupal site is not that crazy or unusual. Of course, if you're just trying to distinguish the pages from each other in some way, sometimes tagging/taxonomy is better than putting them in different content types, but that depends on what you're trying to achieve. If they legitimately have different fields/structure, than you're OK to have 10 content types.
Does that answer your questions or were you getting at something else?