My electric toothbrush had a wireless charger, and that was at least 15 years ago. Induction is not really something new and that's how terrestrial TV and radio transmission works, they all transmits energy wirelessly and have been with us for more than 100 years.
It has no earth if the equipment doesn't need it because it fulfills the necessary safety standards. E.g. kid's toys that run on AC power and have 2-pin plugs require double-insulated power supplies.
Which ones - there are several 2-pin plugs and some of them will stay in the socket just fine.I'd say those 2 pinned plugs are dark age plugs ...