The Russian Messenger (Russkii Vestnik) went through a number of incarnations. The first Russian Messenger was edited by Sergei Glinka from 1808-1820 and again in 1824.
The third incarnation was founded in 1856 by a group of liberal intellectuals, and grew to become one of the most influential of Russia's 'thick' journals (the name came from the hefty size of each volume). Its main editor was Mikhail Katkov. The list of famous works of Russian literature that were first published in the Russian Messenger is dizzying. Tolstoy's major works War and Peace and Anna Karenina appeared in this journal first, alongside Dostoevsky's Crime and Punishment, The Idiot, The Possessed and The Brothers Karamazov, and Turgenev's Fathers and Sons and other writing. See here for more on the treasures published in this journal.
The word otkupshchik means 'lease holder'; they held government monopolies allowing them to sell restricted goods such as alcohol, or, as is probable in this case, act as tax farmers.
Private citizens would be assigned responsibility for collecting taxes, for which they would receive a cut of the money collected. Tax farmers were often seen as corrupt or at least treated with similar contempt to that which parking wardens receive in modern society. Tolstoy hated them particularly as he saw the class of wealthy merchants, otkupshchiks and others as a threat to the power of the aristocracy, and to the natural order of Russian society.
The Battle of Smolensk took place on 4th-6th August 1812. Smolensk, on the banks of the Dneiper, was protected by its fortress-like walls and bastions and believed to be impregnable. The French Grand Army of 180,000 met a Russian force of 120,000. Napoleon was hoping for a swift victory that would ease his way to Moscow, but instead the battle stretched out over three days. The bombardment of Smolensk set the city on fire, destroying its historical centre, which had been regarded as one of the architectural highlights of Russia. Although Napoleon eventually captured the city, he lost 20,000 men in doing so (twice the number as the Russians) and the long battle delayed his advance, weakening his army.
A quire is a unit of paper measurement meaning 24 identical sheets or writing paper or 25 sheets of printing paper. It equates to 1/20th of a ream, and there are ten reams in a bale, the largest unit of measurement.