In essence, you are asking how nationalism, Social Darwinism, militarism and military preparations, and the alliance system helped to bring about a situation in which the assassination of the Archduke could ignite a world war.  Let us look at how all of these factors came out of the Franco-Prussian War and helped lead to WWI.

The Franco-Prussian War brought about two conditions that were of utmost importance.  First, it created a unified Germany.  Second, it caused enmity between Germany and France over the issue of Alsace-Lorraine.  These two effects of the war largely brought about the factors that you mention above.

Once Germany united, German nationalism became an important factor in European politics.  This became particularly true when Kaiser Wilhelm forced Chancellor Bismarck out of office and took over German foreign policy.  The Kaiser was a militarist and a nationalist who wanted Germany to gain what he saw as its proper “place in the sun.”  He wanted Germany to be militarily strong and to have an empire.  As Germany became more aggressive in seeking power, it frightened other countries.

As these other countries became frightened, the system of alliances started to build.  France allied itself with Russia and, later, with England.  Russia also allied itself with Serbia for nationalist reasons (they were both Slavic countries who were threatened by German countries).  This helped lead to a tighter alliance between Germany and Austria-Hungary (also based partly on nationalism since both countries were ruled by Germans).  This alliance eventually included Italy.

As these various countries allied with one another, they also believed that they needed more military power to protect themselves against their enemies.  This helped lead to a spirit of militarism in which they equated military power with national pride.  Social Darwinism was relevant here because the various countries believed that the country/nation that was “fitter” would win in the competition.  War, then, became a potential way to prove that their country/nation was fitter and simply better than others.

All of this led to a situation in which a small spark could set off a great war.  The nationalism and alliances meant that a war between two countries could come to involve more countries.  The militarism and ideas of Social Darwinism helped cause countries to believe that it was important to fight.  The military preparations meant that they were all ready to fight.  Thus, when the Archduke was killed, that relatively minor event set off the Great War.