That would be the German Unification of 1871, when Saxe-Cobug Gotha became part of the German Empire. Before that it had been part of the North German Confederation since 1866. Before that it was part of the German Confederation which was dominated by Austria, which didn't recognize confederate sovereignty. The only significance of 1918 is that is when the last Duke died. Saxe-Coburg Gotha was split between Bavaria and Thuringia in 1920 and dissolved.
No. Like neighboring Bavaria, Saxe-Coburg and Gotha retained its monarchy past Bismarck's unification of the northern Germanic states in 1871. This lasted until the end of World War I and in 1918 Saxe-Coburg and Gotha merged with Bavaria and Thuringen, who then joined Weimar Germany.