The Orwellian vision of perpetual war being used to justify more centralised power and a lack of democracy is, I think, closer to the mark. The more chaos, the more power can be centralised.
Muslims make up close to 20% of Russia's population (the 8.5% figure usually cited is incorrect because Chechnya and Ingushetia were at war when the last census was taken and so are not part of the total given). Islam has been in Russia since the very start of the religion ( a few decades after Mohamed died) and Islamic Intellectuals were encouraged by Catherine the Great. They are nearly all Sunni and most of them live around Moscow and St. Petersburg.
The populations in the South are relatively small although they can certainly cause problems and yes, they are also predominantly Sunni with many of them being part of the Sufi sect. I find the religious history of the Caucuses and Central Asia in general fascinating.
Yep, but the bigger picture is to ensure there is no gas pipeline to Europe through Syria and general instability in the region.