If you just want to duplicate an existing category with a new admin page it would need to do the following:
Have a recordset that selects all of the item where the category id matches the desired category.
You would then need to have a multiple insert that would insert a new record for each of the records in your recordset. You would insert all of the same details for the items except for the category id. This would need to be set to the id for the target category. In the end this would give you a category that has the same items as another category on your site but a different category id listed.
This may not be the easiest or most straight forward thing to get implemented as it will require some custom coding and knowledge of php and MySQL. Due to the custom nature of the task it is not something that is directly supported.
As for the second category that you refer to it does not seem that this would be any different than any other category with items associated. You would define the category then add items to it.
