Multiple sites sharing global templates
Global templates are absolutely possible by taking advantage of the Twig {% extends %} tag. You can read more about template inheritance in Twig's documentation.

If you set up multiple sections, you can assign certain users edit privileges to their appropriate sections.

You can set up your navs and footers as Globals (or use a plugin), you can set editing privileges just to admins. Simply create a header and footer partial template and include them in a main template file that your other templates extend.