Is flight training on Russian planes performed in Russian?
Kind of unclear, but this would be dependent upon the country in which the flight training is taking place. If the training is taking place in Russia, most likely the instructor would speak to the student in Russian. If in the United States, the instructor would speak to the student in English.  As for ATC  transmissions, the only time the flight crew would be required to speak in English would be on an IFR flight plan. Any other time, they would speak their native language on the radio.