#1
What's the theory behind "Russian" sounding guitar music?
The only example I can think of off-hand is the acoustic guitar riff at the beginning of "Rasputin" by Boney-M. (Poor, Poor Example)

What kind of scale/mode would you be using to play that kind of music?
#2
I've never seen anything too "out there". A lot of typical harmonic minor stuff, maybe phrygian. A lot of Russian folk music (whether guitar or not) is more sad than happy. When it comes to acoustic guitar, it's all very simple stuff most of the time, nothing complicated.

I'm Russian btw

Also, this.

http://www.stseraphimschurch.org/we-magazine/statyi2005/guitarrussianstyle.html
#3
Duh-HUH!

The Russian Scales of course!
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#5
Here's a scale that has sort of a "Russian" feel to it. It's called Gypsy Minor

The Formula for this scale is; Root, 2nd, m3rd, #4, 5, b6, 7.

or for the theory impaired; Key of E - E, F#, G, A#, B, C, D#.
There's my way and the wrong way.