Well, if you want private images it is normal that they charge you for it. What I advise you to do is to make the images public and mount the private part as a volume. This way you can upload the images wherever you want without worrying.

Another option if you want the resulting image to have something private is to create as much as you can in a public image and have a script that adds the private part as the last layer.

Apart from the registries you have in GitLab and GitHub if you are looking for something more generic like Docker Hub you have Quay (from RedHat). It works very well and has a pretty nice interface (especially the new one that is in testing).

You don’t really need Cloudflare to have your own domain, you can do everything directly with GitHub.

It is not about leading anything but about having the code in a repository so that it is easy to read/consult/audit/etc.

You can upload the code to any service (it doesn’t have to be GitHub, it can be GitLab, sourcehut, etc…) and disable issues and comments.