Short answers, pulled from the story.
The Mongolian People's Republic was officially named in 1924 following the death of the Bogd Khan. This state existed from 1924 until its dissolution in 1992 when a new constitution entered force on the 1st of February 1992.
Cavalry under Damdin Sükhbaatar captured the capital with Soviet troop support to mark the Mongolian People's Revolution. The Mongolian People's Party had been founded in November 1920 at Kyakhta by leaders including Khorloogiin Choibalsan and Dogsomyn Bodoo.
Mass arrests swept through Mongolia under the direction of Khorloogiin Choibalsan who served as minister of internal affairs and commander-in-chief. Some 20,000 to 35,000 Mongols were executed during this campaign organized by NKVD officials while approximately 17,000 monks were killed.
Mongolia did not join World War II directly but provided volunteers and materiel to support the Soviet war effort. In August 1945 the Soviet Union used Mongolia as one base for its Manchurian Strategic Offensive Operation bringing 650,000 Soviet troops and large amounts of equipment.
The first multiparty elections took place in July after the MPRP leadership resigned in March following demonstrations and hunger strikes. These elections gave the MPRP majorities in both bodies approving transition to market economy before a new constitution adopted on the 1st of January 1992 entered force on the 1st of February 1992.