Scotland Yard is more commonly known these days as the Metropolitan Police, or the Met, who per the name handle policing in the London metropolitan area, but they do also handle national tasks like counterterrorism and protection of the royals. They're the closest thing to the FBI in the UK right now.

Most of Greater London. The City of London has its own police.

Nope because different police are organized for different jurisdictions.

The jurisdictions generally correspond to counties, though some counties pool their resources and share a single police authority between them.