The city of Yaroslavl (Ярославль) is located to the northeast of Moscow, approximately 160 miles away, and is known as one of the Golden Ring cities—a group of historically important cities in Russia’s history. Today the historic parts of the city are recognized as a World Heritage Site.
The noun “lorgnette” refers to a pair of glasses held in from of one’s eyes using a handle. The glasses were typically used at the opera, an upper class source of entertainment. Charlotta’s appearance gives the impression that she is wealthy enough to afford to go to the opera as a governess, signifying the emergence of the Russian middle class, who could afford to indulge in some upper class delights.
Epikhodov is referring to Henry Thomas Buckle (1821–1862) who was an English historian and the author of an unfinished work titled the History of Civilization, in which he sought to state the general laws that govern humanity’s progress, supported by examples from particular nations.
"Humming a Caucasian dance] ..."See in text(Act III)
Caucasian here refers to the mountainous Caucasus region, situated at the border between Eastern Europe and Western Asia. In Russia, a caucasian dance, or lezginka, is a traditional folk dance. Performers wear traditional costumes, which usually includes a sword for the men, and long, flowing dresses for the women.