A seminary is a school that trains young men to become priests and other members of the clergy someday. The clergy is it's own social class in the Russian social hierarchy of tsarist Russia (pre-1917)
According to en-academic.com,
grammarian = freshman
rhetorician = sophomore
philosopher = junior
theologian = senior
The descriptions of the men in their various stages of growth seem to imply that these line up with our contemporary high school years--9th through 12th grade, though may not be the exact same ages.
kibitka--a covered wagon pulled by horses