Regarding the Persian war, it was less a case of imperialism, than a comprehensive step to have more logical, safer border. If they wanted more land, they would have kept fighting past 1826, the Persian Empire was going down anyway. In lieu of that, the Russians accepted less ground, but more safety.
Tatars were made to move on, and this in a very normal fashion, they lost their privileges, lost their protector, and so they also got massacred. I shed no tear for them, no one should shed tears for human traffickers and pirates, never mind the fact they destroyed largely the Hellenistic heritage of Crimea.
Persians were Team B in this, they tried and almost succeeded to get a huge part of the Caucasus, unfortunately, the Armenians wee having none of that shit and offered a much needed local support to Russians. Ironically those who had the more to gain from the Russians, Georgians, decided to stand against them.