He power to create and maintain a police force, which is exercised at the state and local level, is considered one of these powers?

This is a part of the executive power. The three branches of power that were separated according to the separation of powers idea are the legislative, which is the congress, the judicial, which is the court system, and the executive, which is the president that oversees things like other executive agencies or departments like the police, which is a part of the executive branch.