I too would go for the train, as most Russians do. There ae multiple overnight services between Moscow and St Pete, and it saves 2 nights hotel as well. The stations are in the city centres so that avoids airport transits. It's an interestng experience as well. Get someone in Russia to book it for you. Always get a lower level bed, lift the mattress, and put your bag under there and sleep on it.
Yes the toilets do discharge directly on the tracks, as they have done in pretty much every other railway in the world until the last decade. There is no water u-bend so the tracks are visible zooming along a couple of feet underneath your behind !
The metro maps in Moscow and St Pete are changing to show both Cyrillic and western characters together.
Taxis at the airport are still an issue, and in St Pete at least ones you hail on the street have pretty much disappeared.