Step 1: Analyze each statement for its historical accuracy regarding the unification of Germany.
(1) Bismarck manipulated the content of the telegram sent by the Prussian King.
This refers to the Ems Dispatch (1870). Otto von Bismarck, the Prussian Minister-President, deliberately edited a telegram from King William I to make it appear as if the King had insulted the French ambassador. This manipulation was intended to provoke France into declaring war on Prussia, leading to the Franco-Prussian War, which was the final stage of German unification. This statement is TRUE.
(2) Bismarck requested Napoleon of France to remain neutral during the Prussian war with Denmark.
The Prussian war with Denmark (Second Schleswig War) occurred in 1864. While Bismarck engaged in complex diplomacy to isolate opponents, his primary diplomatic efforts regarding Napoleon III's neutrality were more prominently focused on the Austro-Prussian War (1866), where French neutrality was crucial for Prussian success, and the lead-up to the Franco-Prussian War (1870-71), where he aimed to provoke France into war, not secure its neutrality. There isn't significant historical evidence to suggest a prominent or defining request for French neutrality specifically during the Danish war (1864) as a major strategic diplomatic move. Thus, this statement is FALSE.
(3) The formation of Zollverein was the first step enrouted to political unity and unification of Germany.
The Zollverein (German Customs Union) was formed in 1834. It abolished internal customs barriers between many German states, fostering economic integration and a common market. This economic unity laid a significant foundation for future political unity by creating a sense of shared interest and reducing fragmentation. This statement is TRUE.
(4) William-I was the first united German emperor.
After Prussia's victory in the Franco-Prussian War, King William I of Prussia was proclaimed the German Emperor (Kaiser) on January 18, 1871, in the Hall of Mirrors at the Palace of Versailles. This event officially marked the creation of the unified German Empire. This statement is TRUE.
Step 3: Identify the false statement.
Based on the analysis, statement (2) is the false one.