Short answers, pulled from the story.
Bartolomeu Dias rounded the southern tip of Africa in 1488. His crew forced him to turn back before noticing that the coast swung northeast toward the Cape of Good Hope.
The Dutch East India Company dissolved in 1799 due to financial difficulties following wars with England. The company was once the richest private entity in history with tens of thousands of employees and a private army.
Indian troops called sepoys initiated an uprising on the 10th of May 1857 after rumors spread that their bullet cartridges were lubricated with pig and cow fat. The mutiny ended dual control between government and company transferring political responsibilities to the Crown in 1858.
Treaties of Gulistan in 1813 and Turkmenchay in 1828 gave Russia direct borders with Persia's heartlands and Ottoman Turkey's territories. These victories occurred after Russo-Persian Wars ending with these specific agreements.
China signed the Treaty of Nanking in 1842 losing decisively by 1842 signing Treaty of Nanking ceding Hong Kong Island opening ports like Shanghai and Guangzhou. This event marked the conclusion of the First Opium War beginning in 1839.