to 1)
install vanilla LibreELEC, probably one of the nightlies from here:
LibreELEC Alpha/Beta Preview Builds – LibreELEC
Test every possbile scenario and see if you find something that doesn't work as expected. Then report at the "Bugreport" subforum.
For github:
Get your own github account and fork libreelec and clone it to your machine. Build LibreELEC from source or use a nightly. After you have found some issues, try to fix them on your own by changing the specific code. Then compile LibreELEC and see if your changes really fixes the issue you found and that it doesn't harm any other section. If all went fine, do a pull request at LibreELEC and probably it will get merged. That's the best thing to provide help if you are able to code.
to 2)
probably with docker, but I'm not sure. I only know the plexbmc addon.
to 3)
I guess most of this might be found here: Linux From Scratch
I doubt there is a "step-by-step"-guide for building custom linux distros.