Short answers, pulled from the story.
The Tsiolkovsky rocket equation shows that for a rocket engine to change momentum, it must exhaust mass opposite the acceleration direction. Both reaction mass and energy are required for this process to occur in conventional solid or liquid rockets.
The first nitrous oxide-based system flew in space in 2021 using six Dawn Aerospace B20 thrusters launched upon SpaceX Falcon 9 rockets on D-Orbit ION Satellite Carrier. This mission demonstrated non-toxic green alternatives replacing highly toxic hydrazine fuel globally.
Robert Goddard considered the possibility of ion propulsion in his personal notebook in 1906 while Konstantin Tsiolkovsky published the idea in 1911. These early concepts led to modern electric propulsion systems used for station keeping on commercial communications satellites.
Japan launched the solar sail-powered spacecraft IKAROS in May 2010 successfully demonstrating propulsion and guidance still active as of this date. NanoSail-D became the first such powered satellite orbiting Earth confirming solar sail concept viability.
Aerobraking allows spacecraft to reduce high point elliptical orbit through repeated brushes with atmosphere at low points saving considerable amount fuel. This method was done on several Mars missions including Mars Global Surveyor 2001, Mars Odyssey, and Mars Reconnaissance Orbiter plus at least one Venus mission Magellan.