1. What was the immense human cost and horrors Europeans inflicted around the world?
2. How do those affect many countries to this very day?
The Arabs and the Turks conquered much of Europe before they were finally turned back at the gates of Vienna in 1683. They ruled Spain for 700 years. They've ruled northern Africa for 1300 years. And they filled in the gap left by the Romans. The Mongolians conquered nearly all of Asia and Eastern Europe and held them for a couple hundred years.
History is the story of conquest and expansion. Some good, some bad. I'm not going to call them atrocities; death comes with conquest. But the history of European conquest, while containing much bad for those conquered (particularly the Aztecs, Incas, Congolese, etc.) is one of overwhelming good for the world.
It wasn't the Europeans that accomplished this good....it was the ideas that some of them brought with them. And those ideas came out of the Enlightenment: government determined by the governed, individual liberty, freedom of thought, of speech, of the press, of assembly, trial by jury. It isn't possible to overstate how utterly radical these ideas were, and they are why a poor shepherd in Angola can lift himself and his family out of poverty. Or in India, which sees 44 people per minute come out of extreme poverty.
For all of human history, however many thousands of years that is, there has never been anything like these ideas; the literal 0.1% ruled in luxury, while the other 99.9% were serfs, or slaves, and could hope for nothing better, for themselves or their descendants.
So.....I'd say, because, like a virus, the ideas of individual liberty, freedoms, equality, and the like that the Europeans brought with them, that has been overwhelmingly good, and to the degree that a culture adopted those ideas, that is the degree to which they, too, have prospered.