Short answers, pulled from the story.
On the 5th of October 1914, a French Voisin III aircraft became the first machine to shoot down another airplane. Before that date, front-line military aircraft served almost exclusively as unarmed reconnaissance tools.
Roland Garros modified a Morane-Saulnier Type L with metal deflector plates on the propeller blades in March 1915. This modification allowed forward-firing guns without destroying the aircraft itself and led to the development of synchronization gear by German forces after his capture on the 18th of April 1915.
British Hurricanes and Spitfires proved roughly equal during the Battle of Britain thanks to radar-based Dowding systems. These systems directed fighters onto German attacks while allowing the RAF to deny Germany air superiority.
Messerschmitt developed the first operational jet fighter, the Me 262A, serving with Luftwaffe's JG 7 wing during World War II. It proved considerably faster than contemporary piston-driven aircraft but never deployed in sufficient numbers to stop Allied air campaigns due to fuel shortages and technical difficulties.
Soviet Mikoyan-Gurevich MiG-15 fighters shocked American pilots during the Korean War on the 8th of November 1950. These swept-wing designs allowed flight closer to the speed of sound than straight-winged alternatives and forced North American F-86 Sabres into battle with similar transonic performance.