while being a learner,
its illegal for the learner driver to drive without an instructor or 3yr+ licence holder present,
as it invalidates the insurance, [this is what my instructor taught me]
as for the takeover part, normally that only happens if the instructor or licence holder deems the person they are supervising, unsuitable to be driving
[be it nerves taken over too much - reckless driving - the driver is no longer being safe for other road users [car's, pedestrians, road workers]
as for if a supervisor takes over, they should have 3rd party insurance at as minimum coverage.
and you're are correct about the motorways, [duel controls] are needed unless your a full holder, but its always good to learn in your own car.
^ not every instructor will follow this rule, but most do. but it depends mostly on how comfortable they are with your current standard of driving.
[edit: the supervisor wouldnt be driving - on a test it would be the learner. and i guess it depends if the examiner has a licence to drive - you dont need to have a licence to be an examiner XD weird huh... ]
please dont take offence to the overload of infomation but the more you know the better.
glad i could be of help. any more questions feel free to ask, sorry if i take 20 years to respond, [sometimes i can be fast sometimes i take forever]