Short answers, pulled from the story.
The modern Russian police force operates under the name Police of Russia. This entity functions as the successor to the former militsiya and falls under the oversight of the Ministry of Internal Affairs.
The Federal Security Service serves as the domestic security agency for the nation. It is the direct successor to the Soviet-era Cheka, NKVD, and KGB organizations and manages border protection through its subordinate Border Guard Service.
In 2004 there were 760 institutions across administrative divisions including eight prisons and 62 juvenile facilities. Ninety-two pre-trial facilities completed the statistical picture from that period within the system administered by the Federal Penitentiary Service.
The Russian Military Police provides service police functions for all branches of the Armed Forces. They maintain order among soldiers and handle internal military discipline issues while operating under a specific ministry.
The National Guard performs gendarmerie duties supporting regular Politsiya units and handles large-scale riots. Formerly known as Internal Troops, OMON, and SOBR these forces deal with internal armed conflicts when necessary.