Conscription was an ever-present reality for many Soviet citizens from the establishment of the USSR. The Soviet state only allowed for conscientious objection from a few minority sects like the Doukhobors, so aside from health issues, there were few ways to escape the draft. So for the OP's hypothetical Russian peasant (the Soviet Union was reluctant to expand conscription to its national minorities), compulsory military service would not have been something unexpected or extraordinary.

Up to 1935, the interwar Soviet army had two main forces, the krasnoarmeitsy (Red Army) were formal military men and terrarmeitsy (territorials) who were fie year military reservists. The bulk of peasant military experience prior to the 1935 was spent with the terrarmeitsy, who would spend three months of training during the first year of service; two months in the second; and one month in each of his last three years. The Red Army underwent a doctrinal shift and began to transform all terrarmeitsy into formal military units by 1940. The terrarmeitsy provided a rudimentary groundwork for the conscription apparatus to expand greatly.

In 1940, the state passed a new military service law that massively expanded the size and scale of conscription. This caused a great deal of friction within peasant communities as the large casualties
from the Russo-Finnish War had became common knowledge. This unrest led to a greater crackdown on desertion and draft avoidance which only increased after the German invasion.

The scale of the German threat meant that the Soviet state resorted to many of the tactics it used to create the Red Army during the Civil War. Although lines of formal conscription remained, the state employed a wide degree of impressment and the resurrection of opolchenie (citizens militia army). The latter were volunteers and equipped with a hodgepodge of obsolete or captured weaponry. Training time could be as little as a few hours each day for a week before they saw combat. The closer to the front, the more chaotic conscription became; so called-front mobilization entailed military units impressing any military-aged male and putting them into the front line.

The state of conscription was less chaotic inside the Soviet interior, although that is not saying much In September 1941, the State Defense Committee established the Vsevobuch which provided formal military training within all localities of the Soviet Union. It established a minimum of 110 hours of training and opened 15000 training centers. In theory, the conscripts would form a reserve unit that would then be funneled in as replacements. The quality of training was often quite poor and the needs of the front forced
a telescoping of training. The 1943 account of Gabriel Temkin is instructive of this training (or lack thereof) for the Vsevobuch recruit. He spent enough time in his training depot to receive his military kit and no rifles, his trainer told him that he was to learn at the front. He describes his first combat as:

The politruk was right. There were plenty of rifles, ammunition, and hand grenades left by the dead and wounded in the field and trenches, and I was soon to “learn on the job” how to use them. I had not seen yet the first sunrise on the bridgehead when, before daybreak, and with no support from our artillery behind the river, our company was rushed into an attack on enemy positions.

In subsequent combat, Temkin's regiment suffered a thousand casualties.

Sources

Reese, Roger R. The Soviet Military Experience A History of the Soviet Army, 1917-1991. London: New York, 2000.

Sanborn, Joshua A. Drafting the Russian Nation: Military Conscription, Total War, and Mass Politics, 1905-1925. DeKalb: Northern Illinois University Press, 2003.

As a follow up; how likely is it that he will survive until the end of the war?

There is an interesting Memoir that goes into some detail about things you are asking about. "Guns Against the Reich", about an Artillery Officer who was called to serve in the Red Army at a similar age. Petr Mikhin was called to serve in the Red Army, rushed through Officer Training and sent to the front to command an Artillery Company of heavy howitzers. He tells in detail of what it was like being recruited, and even tells about the Political aspects of certain "Frontline" situations.....like for instance, what happens when a Soviet Officer "allows" one of his Howitzers to become damaged. He tells how rushed everything was in the Red Army. People died so quickly, and they needed people so badly that the training for Officers was often poor, and it seemed that they counted on Political Officers to handle a lot of duties that Military Officers should have handled. Transit: Again, Petr discusses this this in the book, but many of the younger men served in something similar to a "home army", where they would have minor military training, but defended areas surrounding their own villages/cities where the fighting was just as fierce!

A somewhat related question.

I've read that the soldiers who suffered horrific injuries, the quadruple amputees (nicknamed "Samovars" after the large Russian teapot) were found to be detrimental to morale in post-war Soviet society and were all (those not permanently hospitalized) sent to Siberia with some nurses and prostitutes and lived there in a small village that was off limits to the general public and foreigners.

Other than that little bit of information, I haven't been able to find out much else about them. Anybody know more?

Would a Russian in 1941 be considered a peasant?

What is the minimum age of getting into the Soviet Army at the time?

I don't have anything to add to /u/kieslowskifan's excellent answer, but wanted to recommend Catherine Merridale's book Ivan's War: Life and Death in the Red Army, 1939-1945. It's a fantastic look into the average soldiers life before, during and after World War II.