Yep, a fuse is mandatory due to ring mains being 30A and the plugs being rated at 13A max only.
This clearly does not apply to wall warts as they can have an internal fuse (and must have one to meet BS!) although some cheap supplies seem to rely on the primary winding of the transformer! (again not allowed!)
You can use a plastic earth pin on items which are double insulated.....but any metal earth pin must have no sleeving unlike that shown in the pic!
The reason behind the no sheathing is because the whole setup is designed so that when inserting and removing a plug the earth contact is the first to make and the last to break. As a result, some older wall sockets have the earth contact very close to the surface and on the item in the first post, there is a risk that any item connected using this lead would not have any earth connection at all because the conatct in the socket would be sat on the insulated section!