Hmm. Interesting thread, particularly since my current WIP is set partially in St. Petersburg in 1788. So I guess I'd have to say, judging from the information I can't find, anything about St. Petersburg in 1788.
*sigh*
Since the Russian aristocracy was so obsessed with Western culture and standards, the most difficult thing to discover is how they bridged the gap between a Francophiliac court and the Russian side of life outside of the Court. Keeping in mind that my research is still ongoing, this is what I'm having trouble locating:
1) good historical data about how Russian nobility before the Decembrists balanced their Russian culture with European fashions, etiquette and so forth.
2) the impact of Catherine II's age of enlightenment upon the nobility
3) the role of women within the aristocracy--and not just historical figures like Princess Dashkova.
I would think that there has to be some kind of balance between the realities of life in Russia and the Potemkin village-like devotion of the aristocracy to Western culture and ideals. unfortunately, I'm not finding much evidence of that at the moment.
Wow, now that was a coincidence. I'll try to briefly answer your questions the best I can and see if I can come up with some research links. This seems to me an interesting and accurate book:
http://www.amazon.com/dp/0253208424/?tag=absolutewritedm-20
(You can read it for free on Google Books, but the link is so huge it doesn't fit here)
http://www.amazon.com/dp/0754605051/?tag=absolutewritedm-20
(Also available for free at Google Books)
http://www.amazon.com/dp/0156701502/?tag=absolutewritedm-20
(this one can also be read for free at Google Books)
1. Basically, they had nothing to balance. The Russian culture was considered "low" and "vulgar" and the Russian nobility strived to be as sophisticated as their European peers. The Russian nobility led a life of their own that didn't have (or at least strove not to have) anything in common with the Russian traditional culture of the time. The gap between the cultures of the lower classes and the nobility only deepened ever since Peter the Great and was, in fact, one of the reasons for the 1917 revolution. It resulted in a society where higher classes led a European lifestyle while the low and especially peasant classes led a life comparable only to that of the poorest African countries of today. In 1743, Elizabeth officially forbade the use of Russian national costumes at masquerades as "offending". In Eugene Onegin (just pre-Decembrists), Pushkin mentions that his noble-born heroine Tatiana wrote her love letter to Eugene in French because she didn't know enough Russian (naturally, because it was considered the language of lowborn people). If you remember the bit from The War and Peace when Natasha dances a Russian dance in the hunters' lodge, the whole conflict of the scene is in the fact that she'd had nowhere to learn it from, she'd never seen a Russian dance before, and everybody present are stunned by the fact. They didn't have to bridge the gap because they didn't need to: they were on their own in their little pseudo European world, and low classes with their Russian culture, on their own too. Of course, the nobility were
sort of familiar with the Russian culture through their nannies, servants, through their lowborn childhood playmates, but they definitely didn't live it.
Itv wasn't even European vs. Russian, as it was noble vs. low. Just days after the French revolution, the new French fashions were officially banned at the Russian court as "low". Part of Pushkin's phenomenon was in the fact that he finally familiarized Russian literate classes with the Russian folk culture.
You can compare it to the mentality of the American South: would plantation owners be interested in their slaves' culture? The same was true about the majority of Russian nobility.
2. I've done some research on the reign of Catherine in the past, so I can probably answer this one. The impact of her era upon the nobility was overall not very good. The most amazing thing about Catherina was that she, ethnic German to the bone, re-trained herself to become one of the most Russian rulers ever. She worked hard to study the language, culture and history, and became a passionate Christian Orthodox. But the court in her time led a highly indulged, spoiled existence, she forgave too many offences and despite all her projects and best intentions (and she was a lovely character overall), the country during her rule lacked discipline. Bribes ruled big time, at all levels, and she just laughed. That's why the country suffered such a terrible overhaul during Paul's rule who had to control an inert mass of uncontrollable nobility who saw the meaning of their lives in pleasure and self-indulgence, not in improving their country.
3. Women were overall more connected to the ethnic Russian culture--through their nannies, maids, wet nurses, etc, as well as instinctively. But don't forget that the Russian society was very organized, not to say militarized, by the ranks system, it was a man's world, the world of clerks and officers, and women had no place in it. They were always clever in their influence, but there was a zero chance of them excelling at anything out of their domain. Profoundly religious, good mothers and wise wives--that was all there was to it. They guided, not ruled. But being wise and clever, they surely had lots of influence.
I'm afraid my answers are shallow and superficial (which is the same) but hopefully they give some idea, and the sources can help you in your research.
Good luck!