Height and Sticky
You can adjust the header height and set whether it should 'stick' to the top of the page upon scroll.
Appearance > Customize > Header and Navigation > Header
Layout
There are also some layout options which allow you to move elements around.
Appearance > Customize > Header and Navigation > Navigation Layout
Tools
The site icons on the right can be enabled via:
Appearance > Customize > Header and Navigation > Site Tools
Header Colors
These can be tweaked within
