Correct me if I'm mistaken (My wife does..) but the original question was about the legal position. Which is easily answered & has been.
If you're a student on a driving course, they will insist upon helmets from an insurance & communication perspective.
There may be confusion for future owners from a driving licence angle, but the car is classed as that - a car. Seatbelts are as mandatory as any other car use.
Yes but the November copy of Miscellany has an article on the experience, and I quoted directly from it. The communication and insurance issue is another matter entirely and to instruct - one has to communicate.