re: To have an admin for each category where they can only manage users in that category.
Sorry, no. All admins that have permissions to edit the directory entries will be able to edit entries in all categories.
re: To make it so that when a member logs in they see only members in there category and cannot see or search any other category members?
Sorry, no. There is no way to prevent what a user permission to view based on category.
re: Just to make sure that link will allow any member to edit only their entry.
Yes. When a user is linked to an entry by Link, they will only be able to edit their entry.
I hope this answers your questions clearly and thoroughly.