Easiest is to create new function profile for this one user, copy existing function profile to new one and remove Open item edit function from others function profile.

How can I make the copy without having to  add the function manually one by one?

Make a copy of function profile for the specific user and modify the original one (by removing assess rights) and specify rights for the advanced user.

When I make the copy. This is the original.

When I make the copy the functions do not transfer over. Am I doing something wrong?

You need to copy the authorizations over after you copy the functional profile.  It is in the action bar-> Merging.