And dear me, the demographics are a nightmare... Does the Chechen republic cover all of the Chechnya region? If so, I hope it's not being run as a nation-state; Chechens would be in the minority. From what I can tell, it also includes Stravropol, which would make the region have an extremely large Russian plurality (say 40% or so) if not more. The Ossetians, Balkars, and Kurachai (among others) wouldn't be desiring Chechen rule, either. And I'm not sure if Chechnya by itself will be able to maintain independence, as it would be completely surrounded by the IEF.
Dagestan likely won't join in the revolution lead by the Turkic group, as the largest Turkic demographic would be between 10-20% of the population, with the rest being smaller. The largest would be the Avars by a factor of two. The region is so fragmented, culturally, and maintaining independence as a united republic would be difficult, especially as many of the region's independence movements are being lead by Turkic pan-nationalists. Dagestan won't go and join the Turks; at best, it becomes a war-torn hellhole as all of the various small ethnic groups start fighting one another.
It's basically the same as OTL, really. The Caucuses are a crisis point because of the large concentrated demographics that are located next to one another and don't generally care for one another, either. And that's putting it nicely.
As to the point about Kazakhstan/Kazakhia; OTL, in 1959, the Russian percentage of the population peaked at about 42.7% of the population; with Belarussian at 1.2% (mind you, they are considered the same, so 43.9% total) and Ukrainian at 8.2%, you had near an outright majority. Now, without the Second World War, the purges, and a generally more successful and peaceful Russia to this point.. (and without the forced repopulation & Russification of Kaliningrad, etc), there would have been an uptick in colonization. (Mind, the Russification of Kazakhstan also took place during the period of the USSR, so there were some forceful population movements, but there also was the concept of an ethnic homeland) The Russian/Belarusian alone could account for 50%+ of the population of Kazakhia at the same time, and with the Ukraininan population added to it, it could be approaching 2/3s.
Of course, that population did trail off, but it could lead to a situation that the dwindling population of Kazakhian Russians is near 45% rather than 34~% as of OTL in 1989. If the colonization was more natural rather than forced settlements, it could actually have kept growing early on, slowly, only seeing a near majority around 1980 instead of near 1960 as per OTL. That was when the Kazakh birth rate overtook the Russian one, not counting emigration from Kazakhstan proper.
That's just for Kazakhia; there could be similar issues throughout many of the IEF's border provinces. There could even be sizable Machurian minorities throughout, along the same vein. I imagine a lot of southwestern Armenia has a large Russian population, similar to how a lot of southern Bessarabia.
It's a mess. A big bloody Yugoslavian mess.