Does the supervising driver have to be insured on the car the learner is driving as well?

The supervisor does not need to be insured unless he's going to take control of the car. So as long as you're sitting in the passenger seat, you'll be fine but if for any reason you need to sit in the driver's seat and drive, then you'll need to be insured on the car as well.

Not really as @gices has said above. Most people do not worry about this because they have comprehensive insurance and most policies on this level of cover have the "drive another car with owner's permission" clause but you don't necessarily need to have insurance yourself to supervise a learner unless you'll be driving as well.