for 3) you might want to add that massive amounts of stupidity on the part of various Allied commanders both at the battle and in the battles leading up to Austerlitz. Austerlitz should not be looked on as a just a single brilliant battle (though it is), but rather the climatic finale of masterfully executed strategic maneuvers. Quite a bit of luck too. Napoleon couldnt have counted on his opponents being as dumb as they were. Never ever make a plan that counts on the enemy making a mistake.