Not in any great number - there was petrol rationing from 1939 and most of the younger drivers were eventually called up - and there was no training for 'the knowledge' for women to be able to take over. So most were used for essential/official journeys and they were difficult to maintain as production of parts stopped. Many London Taxis were requisitioned to assist the London Fire Service, and could often be seen pulling pumps and ladders throughout the capital - but were not really up to the job, so that was largely abandoned as an idea. At that time they were not necessarily black - and still known by the proper name Hackney Carriages (or taxis after the meters they were obliged to use).
Yes
Yes
Of course.
Of course...