The Hundred Days Offensive Jul–Nov 1918 was the costliest
The Ludendorff offensive other wise known as the spring offensive was a German offensive on the Western Front intended to win the war before the American troops that had begun arriving in France could fully deploy.
I'm unsure of how far they advanced
Kaiserschlacht was the last German offensive and was a series of German attacks along the Western Front.
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British believed that most Southerners were Loyalists and that if they gained territory in the South, the Southern Loyalists would hold it for them. Believed that large number of Southern slaves would join them in return for promise of freedom.
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It didn't consider the population sizes of the states
Emperor Justinian reconquered many former territories of the Western Roman Empire, including Italy, Dalmatia, Africa, and southern Hispania.
The completion of the first transcontinental railroad in 1869 encouraged settlement of the American west by proving easier travel and it took less time.