Spiridovich confirms what Lili Dehn said. He also says that she spoke Russian perfectly but with an English accent. She spoke English with Nicholas and with the children at home. English is really the language Alexandra considered her "native" tongue. At one point, in fact, she was quite concerned that the children were beginning to speak English with a slightly Scottish accent picked up from a Scottish tutor, which, (my apologies to Tsaria) she found unacceptable! When with the children in the presence of others, she usually spoke to them in the language of those people, lest it appear rude that she was saying something to the children that could not be understood by everyone. As for the Court, it depended on the occassion and specific person. French was the official Court language, but in informal circumstances she would often talk to them in another language, Russian with Anya V., German with German natives, English with old friends, etc etc.
As for Russian, in my experience it is easy to learn basically but impossible to master as the grammar rules are endless and complicated!