Hi and welcome!
1 The game is programmed in C++, although it's mainly plain C.
2 Handmade Hero is written from scratch; it doesn't use any preexisting engine. Teaching how to do that is actually the whole point of the project.
3 The first few weeks of the project were devoted to writing a platform layer to uncouple the game code from the operating system. The rest of the platform layers will get written when it's time to ship the game. In the meantime, people running OSs other than windows can follow the series using any of the
available alternative platform layers.