What was life in Mongolia like under the communist regime? How repressive were they compared to the USSR? Was there a secret police force similar to the KGB? Did Mongolia have any independent foreign policy goals at the time? How did communism end in Mongolia?

Adapted from an earlier answer of mine:

Outer Mongolia had declared its independence at the time of the 1911 Chinese Revolution (and was under a regime led by the Bogd Khaan), however the Republic of China had made moves to reclaim the territory (technically the Republic of China has still not given up claims of sovereignty over Mongolia). Chinese troops had made some progress on this front until the outbreak of the Russian Revolution and Russian Civil War really stirred the pot.

A White general, Baron Ungern-Sternberg, was based largely around the Russian Far Eastern Railway in Manchuria, and in 1919 he pushed out the Chinese forces from Mongolia and assumed control of the area as warlord (and as part of a larger strategy to attack the Baikal region). He was more or less supported in this adventure by the Japanese, who occupied a large chunk of the Russian Far East during the Civil War period.

Once the Japanese finally withdrew, and the Red Army/Bolsheviks had defeated larger White armies, they eventually set their sites on Mongolia, which was invaded and occupied in 1921 (Ungern-Sternberg was captured and executed). A Bolshevik-inspired Mongolian People's Party assumed control of the area, but kept the Bogd Khaan, the Buddhist leader who had originally declared independence ten years earlier, on as head of state.

When the Bogd Khaan died in 1924, a Mongolian People's Republic was established. It roughly followed the timeline of Soviet history from then on, attempting collectivization in 1928, conducting its own Great Purges, and joining in the Second World War (the Battle of Khalkyn Gol in 1939 was between the Red Army and its Mongolian allies and the Imperial Japanese Army). It pretty much continued on this mirror path until Gorbachev's reforms led to Mongolian perestroika and glasnost, and the communist regime was overthrown in a popular revolution in 1990.

Throughout this period, there was a significant Soviet military presence in the country. As late as 1990 there were some 55,000 Soviet troops stationed there.

For a long time, it was considered a Soviet satellite/puppet state, especially by China. It took until 1961 for Mongolia to be admitted to the UN as a member state largely for that reason.

Some sources:

Peter Hopkirk's Setting the East Ablaze: Lenin's Dream of an Empire in Asia has a chapter on Ungern-Sternberg

Sviat Soucek A History of Inner Asia

As a general aside, communist-era Mongolia is a really understudied subject, as it kind of is removed from the orbit of East Asian history in this time, but also is a very distant satellite from the perspective of Russian-based Soviet history. It's also not technically "Central Asia" in the way that term gets framed for regional studies (ie, the five former SSR "Stans") and Soucek's history is one of the few that tries to tie all these sub-pieces of Inner Asia back together.

EDIT: ooh! Apparently there is a volume of essays by historians edited by Stephen Kotkin and Bruce Elleman titled Mongolia in the Twentieth Century, which looks interesting. However even this volume (which has contributions by Russian and Mongolian scholars) focuses a great deal on the international relations and diplomatic history of Mongolia, the period leading up to Soviet domination, and the post-1990 period, but doesn't have a lot dedicated specifically to domestic issues in the Soviet period.