Trying to understand 警視庁

Japanese Language Questions
1

What exactly is a “Metropolitan Police Department”?
Is it just Tokyo’s Police Department, or does every city/prefecture have its own “Metropolitan Police Department”?

2

Strictly speaking, in Japan, only Tokyo is classified as a “metropolis.” So that’s why the word metropolitan can be thought of as singling out Tokyo. But 警視庁 is just the name of Tokyo’s police department.

3

On the same token, there is a “Metropolitan Police Service” in the UK but it also only refers to the force in the capital.