Helm Repo: can it host dockerfiles and other image-building artifacts
Well that's a legit question IMHO, but there are multiple way of doing things (and no one is worth than other).
1- Everything from dev to prod at the same place
If you want to grab everything from dev to production in a single project, it's possible, but you cannot build the docker image from hell command.
Helm is only here to organize, use template in yaml and sync releases following kubernetes file structure.
You can follows helm repository structure and add other scripts, but you have to execute steps in the right order: build, push, deploy
2- The &quot;regular&quot; way to do
I more often saw a separation of production configuration files and application files.
What I do is:

One repository which carry my application source code + everything for the CI (test, build, docker file)
One repository which carry my helm.charts for all my infrastructure.

Choose what suits the best for you, but keep in mind that helm is a templating system for kubernetes yaml files, so it will not build the docker image.