Seven Things You Need to Know About Chechnya and One Thing You Really, Really Need to Remember
5) And Dagestan? That's another one of those republics?
Correct. Just to the east of Chechnya, Dagestan has actually seen a relative uptick in separatist sentiments and violence recently. Kadyrov, for what it's worth, seems bent on consolidating the greater North Caucasus area under his control, but the Dagestani president still has enough of Putin's ear to keep the status quo as is.
6) Should we be concerned about any potential continuation of a Chechen War in America?
Uh, no. While the Caucasus Emirate has enjoyed a healthy media presence for some time, there's little remaining threat they would seem to pose within Russia, let alone America. Furthermore, there are no logical, logistical goals met with the brothers' bombings within Boston; unlike al-Qaeda, Caucasian Islamist sentiments are confined to establishing an emirate within their traditional homeland, rather than some grand schema of caliphates and worldwide domination. Thus, when you see people claiming that the "Chechen War Has Come To America," tell them to go away. (Note: This doesn't preclude these brothers from tying their attacks to some Chechen separatist sentiment. It's simply that their actions will play no role in furthering that movement, and will likely only encourage Putin and Kadyrov to further their crackdowns.)
7) Anything good I should read on the region?
In addition to this -- and this! -- there's always Leo Tolstoy's seminal The Cossacks, which details the mid-19th-century incursions of the Cossacks, imperialist Russia's front forces, into the northern Caucasus. (Tolstoy also had some nice run-downs in the book of the Crimean War, which saw the first forms of war reporting.)
8) What's the difference between Chechnya and the Czech Republic?