The item that's not true: a) Bismarck wanted war, even if he had to start it.
Bismarck proved to be quite adept at maneuvering other nations into declaring war against Prussia, so that Prussia could be seen as defending its own interests rather than as an aggressor.
The exchange between the French ambassador and King Wilhelm I happened at Bad Ems in 1870. It was a discussion regarding the vacancy on the Spanish throne, and the ambassador was seeking a pledge from the king that Prussia would not place any member of the Prussian royal family into the running as a candidate for that throne. (This was after Prussia had withdrawn the candidacy of Prince Leopold of Hohenzollern-Sigmaringen, who was related to Wilhelm I.)
After the king (via Heinrich Abeken of the Prussian Foreign Office) sent a telegram to Bismarck, Bismarck published an edited version of it that made it appear that there were insults in the conversation. It was enough to provoke France into declaring war, because the situation between the nations was already tense enough to be easily pushed over the edge.