Thanks for reaching out.
No, header builder will not overwrite any settings you made in Theme Options. It will only override the standard header with your custom pro header once you assign it globally or page specific. I'm not sure about what you mean by publishing, but I assume making it live, please check this
You can either click the specific page to assign it, or click Make Global to apply it globally regardless of page. That's after you created your header.
It's the same on footer, but I'm not sure about your question about the content builder as I see from your other thread, you're already doing it and familiar with the content builder.
There is only one builder for header and footer, but there is no strict requirement for the content builder. You can use what's there (eg. cornerstone), or visual composer.
Please check this for more information https://theme.co/apex/forum/t/pro-header-and-footer-builder-introduction/103, https://theme.co/apex/forum/t/x-to-pro-conversion/104