You have 3 templates available for use on the School subsite: Index School, Subpage Default School, and Subpage Fullwidth School. The site has its own color picker as well which will only change the colors for these templates.

Because the templates are duplicated from your main site, everything should work similarly to how youre used to them working. There are link lists specific to the school site that control the School logo, the icon links, the recommended resources, the what to expect links, and the social links that you can edit by going to Content > Link Lists in the CMS:

You will want to use the school templates for any pages on that site so that the navigation works properly.