>It's probably easier for a Russian to understand other Slavic languages, considering how many of these false friends were actually true ones once upon a time. For example, our teacher would chide us every time we'd say "otvorit" - no, that's not Russian, you should say "otkrit"... except then I find that Tolstoy used "otvorit"... And there are other examples.

Your teacher were right and wrong at the same time. "otvorit" is a Russian word but it's not used in everyday language.