Is Polar Lights observation possible at the latitude of 56° N? Back in 2002, me and my friends observed a green glow in the sky at night in the form of giant slow moving spurts of flame, looking more dense near the horizon and more blurred at height. It was surrounding the area, not just on one side, as I see on most of the imagery available. It was bright enough to see for several people sitting around a bonfire.

Is it possible for the natural phenomena, 'Aurora Borealis' take place as far south as 56° N, 37° E; in a Moscow suburb, Russia?
Yes. The Aurora form in a ring, roughly centred on the Magnetic pole. The pole does wander slowly, but it has been located in the Canadian Arctic for some time.

As the pole is on the American side of the Arctic ocean, aurora are seen at lower latitudes in America than in Russia, nevertheless, when a powerful solar storm occurs, aurora can be seen at surprisingly low latitudes, even into the subtropics, as Wayfaring stranger notes in her comment. 

Aurora in Moscow is a notable, but not exceptional occurrence, as this news report indicates http://www.themoscowtimes.com/article/507096.html