Learn to read cyrillic letters. This takes 20 minutes and will greatly help you get around. This web site assumes that you have learned cyrillic and gives no English versions of Russian names.
Walks stairs with great care. Stair steps tend to be irregular. If you don't pay careful attention, you can easily fall.
Russian airlines usually have a 20kg luggage weight limit. You have to pay for all extra luggage separately on each segment of the flight. S7 have a cashier at check-in in Frankfurt who does nothing else but collect fees, so this is serious. The limit includes hand luggage. Accordingly, hand luggage is weighed at check-in. However, airlines tend to make an exception for laptops. This means that weight of the laptop is not included in the total. I have told S7 twice in Frankfurt them that my backpack contains a laptop and it was not weighed. I was lucky. Only general rules are posted on airline web sites, so looking there is not helpful.
When you have checked luggage, keep the stubs for the luggage with you. It is general custom in Russia that these are checked when you leave the baggage claim area.
Never take a taxi, unless when accompanied by a Russian.
Laundries are virtually unknown in Russia. Everybody has a washing machine. Therefore, don't burden yourself with extra clothes. Your host can easily wash your clothes for you.
When you see drunks, walk away. If you can't walk away just fall silent so that they don't see you are a foreigner. Most encounters with drunks are harmless. But they may get aggressive. You don't want to take a chance.