My understanding about Mormon beliefs is that they do serve in armed forces in the country where they live.
Also I may be incorrect but, looking at this question, it seems that Mormons hold the United States in an especially high regard among nations. This can also be seen from the talk "This Nation Shall Endure" (by Ezra Taft Benson, President of the Quorum of the Twelve Apostles, in 1973) linked to the accepted answer to the question.
So the question I wanted to ask is about Mormons living in Russia (where, according to this page, the church has 23,180 adherents).
Edited to a single question:
If a war broke out between Russia and the USA, would Mormons in Russia be instructed to not to fight, considering perhaps reasons such as that it could destroy the United States constitution?