In the U.S., different organizations have different standards. There are 2- and 4-year criminal justice university programs, but many police departments only require a high school diploma. A criminal justice degree or other related degree is usually a plus even if it's not required. As an example, the Minnesota State Patrol requires the applicants either have a 2- or 4-year degree in any subject or be a licensed peace officer (which could have happened through a criminal justice degree or through a police academy).

Most large cities have their own police academy or there's a regional academy that several cities use. Police academy is usually three or four months of intensive training that new recruits go through (a little like boot camp for the armed forces). After graduating from an academy, the officers are sometimes rotated through probationary assignments and then given a more permanent assignment.

Detectives and other specialists are generally promoted out of the ranks of police officers.

Not always. In the US, more common is a sort of police academy. Actual higher education is not really required.