Nelly: lit.,
Batyushkov's works: K. N. Batyushkov (1787-1855), Russian poet
Turgenev: I. S. Turgenev (1818-1883), famous Russian novelist
lime-flower tea: a Russian folk remedy
I can't think or feel: modern audiences, with a modern view of adultery, may consider Helena insincere here and thus disregard what she is saying, but it is more complex than that. Although she is falling in love, she cannot say it openly, since she is married to another. That is not to say that adultery was less common then, but it was not openly approved.
Barring the way: The doctor's crude persistence might not seem in character to modern audiences, but evidently this is exactly how Russian men behaved. ACT III
at the Conservatory: Helena must have been a very good musician to study at the world-famous St. Petersburg Conservatory
forget myself: This is a difficult speech, as Astrov is unconsciously making love to Helena, while Helena's feelings must obviously be in great conflict. At the same time, the whole speech is ironical with its pretensions to art and nature and painting of Russian history.
an inspector general is coming: Russian audiences would immediately recognize the joking reference to Gogol's satirical play 'The Inspector General'
summer cottage in Finland: a
and not Turks: In the 19th century, Turkish law allowed a husband to retain the dowry even if his wife died
Schopenhauer or Dostoyevsky: Arthur Schopenhauer (1788-1860) was a German philosopher and F. M. Dostoyevsky (1821-1881) was a great Russian novelist. (A bit of comic irony here, because each was a great pessimist about success in this world.)
Oh, Nanny, Nanny!: Oh,
Mama! What should I do?: The word translated as Mama is
brush of Ayvazovsky: I. K. Ayvazovsky (1817-1900) painted stormy seas and naval battles, Chekhov visited his estate in 1888 and described him as an old man married to a young and very beautiful woman
You're full of beans: lit., 'you're a clown full of peas'