At least one of the plays was a short one-act play "Packing Up" by Henry P. Grattan from 1904. It was a broad comedy sketch which Alexei's tutor Charles S Gibbes would have known as an educated Englishman. The performance of this sketch was mentioned in Frances Welch's book on Gibbes whose title escapes me (easily found out). The playlet as acted in Tobolsk is perhaps best known for the scene in which Anastasia's rump is accidentally exposed to the audience, resulting in great mirth all around. A semi-famous IF anecdote, you might say.
I think there were at least three or four plays performed, generally on Sundays, including one by a Russian author (Gogol, Chekhov?) and at least one in French, directed by Gillard naturally .