It's never explained how Lukashka and his men return home from the Sultan's palace after the road they took to get to the palace is destroyed.
It's never explained why Lukashka is apparently the only man in the village who can read and write.
It's never explained why the villagers and the Turks are enemies. Ironically, the Cossacks fought for the Turks in the Crimean War, which ended 7 years before Leo Tolstoy published the novel the film is based on.
It's inconceivable that the Sultan would mistake Lukashka's letter as coming from the Tsar, and break the peace struck between them by having his men attack the Prince's carriage.