No. I have comprehensive insurance to drive my own car and my policy allows me to drive any other car not owned by me. However, if I was to blame for an accident whilst driving another car my insurance company would cover the third party claims but there would be no insurance to cover the car I was driving.
No. The requirement is that you must, as a minimum, have cover for third party claims against you. Thus, as previously stated, your insurance would cover the third party claims.
You would not be able to claim anything for damage to the car you're driving, but you are legally OK to drive it.