Byzantium/Constantinople was conquered in 1451, but the empire continued to decline starting around the 18th or 19th centuries. It officially died in WWI. As for how long it was a major threat to Europe, the empire's prime was the 16th century, under Suleiman the Magnificent.
Few events have a worst impact than the ww1.
The French and Indian War impacted the colonies economically. As a result of the war, the British were able to expand their influence in the Ohio Valley. This meant the British would profit even more from the lucrative fur trade now that France had left the area.
