Enable ssh in your dockerfile and you are good to go there, see this one as an example: https://hub.docker.com/r/ducatel/visual-studio-linux-build-b...

Regarding headers/libs you would need to manage that yourself, I normally scp them down locally and add to my Intellisense paths.

Regarding the kernel that isn't something I've played with much, I've been able to load the source but I have not tried any debug scenarios there.