I used to teach a Russian millionaire's wife English, but it was quite a while ago, and I expect that things are much closer to the way they are in the west, now.
If he's going to people's houses, a lot of people ask guests to take off their outer shoes and put on slippers. So nice, warm socks with no holes in.
There may be a lot of vodka drinking, where you drink appropriate toasts in turn. I have to say I find this tedious. You need to be prepared to make appropriate toasts, as they may suddenly turn to you and expect you to say something, but I don't know what those would be any more - it always used to be that 'friendship between nations' went down well, but this may be dated. Perhaps its all 'lets make money' nowadays. If he's with a millionaire, the vodka should be safe - you need to avoid drinking homemade vodka which can be lethal (literally, not metaphorically).
Also, some jokes / funny stories of the sort that translate easily might come in handy.
Also, might be worth being a bit sensitive about the Mafia, etc, not making jokes about this, not seeming excited in a voyeuristic way about Russia being overwhelmed by violent crime and generally staying off the topic.
And Russian women's fashions used to be rather more 'in your face' than UK fashions. Try to avoid staring. 