Short answers, pulled from the story.
Hideo Kojima created the Fox Engine as a psychological experiment disguised as technology. He declared his intention to build the best engine in the world and named it after the fictional military unit FOX from the Metal Gear series.
The Fox Engine mystery began on the 2nd of March 2012 when a mysterious CD labeled Fox Engine Lighting Sample appeared on the Development Without Borders website. This event challenged the public to distinguish between reality and simulation through photorealistic images.
The first commercially released title using the Fox Engine was Pro Evolution Soccer 2014 which launched in 2013. This release followed the engine's ability to break the chains of single-platform development for Kojima Productions.
Konami discontinued the Fox Engine after seven years of use on the Pro Evolution Soccer series. The decision came as PES Productions focused development efforts on the PlayStation 5 and Xbox Series X consoles.
The Enders Project was put on indefinite hold due to the underwhelming sales of Zone of the Enders: HD Collection. Kojima confirmed work on the project began on the 25th of May 2012 but the cancellation highlighted the risks of investing in new intellectual properties.