I'm trying to connect Apple homekit to a nodemcu board, I found a tutorial that works on my computer, but I wonder if there is a way to download and run Node.JS on a NodeMCU board (ESP8266)?
I think you are misleading nodemcu, which is the firmware for ESP8266 boards that interpret the lua language , with javacript runtime node.js, which runs on computers.
So the answer is: you cannot run node.js on ESP8266.
Espruino . HiLetgo NodeMCU ESP-12E .
https://github.com/mertenats/NodeMCU-and-JavaScript