Re: Stalin's speeches
That's right. Stalin made a huge lot of noise against "rootless cosmopolitans". It became a highly derogatory term and an excuse for further repressions. But Stalin's anti-cosmopolitan push happened slightly after WWII, not during the great purge.
I do remember Hitler ranting about "cosmopolitans" in Mein Kampf, albeit not as extensively as Stalin did in his speeches and books. But I'm reluctant to read through that drivel again to refresh the memory.
Anyhow. As Voyna i Mor pointed out right in this thread - fights against cosmopolitanism were invariably part of anti-Semitic campaigns. Both Hitler and Stalin seemed to associate cosmopolitans with Jews, and it's far from the only thing these distinguished gentlemen had in common.