Can I add a search bar outside of the header?

The hero module and search results module both allow you to configure a search bar on any page

Adding search to the hero

From the hero module, below the Basic Information settings, check the box for Search Input:

Once checked, the Search Settings section will be revealed and you can configure the settings accordingly.

Adding the Search Results module

The Search Results module can be added to any page using the drag-and-drop editor, the search settings are unique per module/location.