City of London is the financial district of London. It's where all the biggest office buildings are. So this is saying that in that neighborhood where lots of people commute to every day, there are more bikes than cars.

London itself is a sprawling city, that extends from the urban Central London (which is what most people think of when they hear London) all the way out to suburban homes.

It's essentially a local council area. There's also the city of Westminster next door (although that's a bit bigger). Most parts of London are called "London Borough Council." It's basically the area that London used to be under the Romans.

there reason is to tax dodge essentially. Its allowed its own laws (to an extent) which means its heavily used to funnel money to tax havens.