I'm going to Tokyo from London as a Norwegian citizen, it's a direct flight from Copenhagen to Tokyo. Do I need to apply for a transit visa to fly over Russia and reach Japan? Can an aeroplane company handle the visa procedure for me or do I have to apply for it myself through the embassy in London?
I've never heard of any situation in which you need a visa of any kind to fly over a country. You would only potentially need one if the flight was planning to land in Russia, in which case it would depend on your precise itinerary, citizenship, whether you needed to leave the transit area, etc.
Imagine the confusion if you had to apply for transit visas for every country you overflew - on a long flight there could be dozens. The international community is sensible enough not to demand that.
In theory, if your airline provided the passenger manifest to Russia before the flight, and the Russian authorities saw your name and decided they did not want you flying over their country, then they could refuse permission for the flight to enter their airspace with you on board. In that case the airline would most likely just refuse to let you board at all, so that they could fly over Russia as planned. But this is improbable; and if it did happen, having a visa wouldn't help.
If for some reason, your flight makes an unscheduled landing in Russia due to an emergency or other unexpected event, you'd either be kept on the plane, let off the plane but kept in a closed area like the airport lounge, or issued an emergency visa. You still wouldn't need to have applied for a transit visa in advance.
You do not need a visa for flying over a country. Even better, for connecting flights you can often even land at an airport and change the plane without a visa of the country the airport is in - although this does seem to depend on the airport and the terminals used by the flights in question and it's prudent to verify this with the carrier or the airport in advance on every flight. You obviously will need a visa for leaving the airport.
If you were to land and connect to another flight a few days later you will in general need a visa, but in some cases even that is not necessary. If you land in Moscow, you can stay in the Novotel Moscow Sheremetyevo Airport Hotel without a visa:
The Novotel Sheremetyevo Airport is the only hotel available for transit passengers who do not wish to obtain a Russian visa, although they are accommodated in a separate part of the hotel and kept under constant supervision.