Where are the Heading 2, Heading 3 et. cetera styles in Word and why are they not showing up?

To make these show up, you need to click on the bottom right of the Styles tab. This brings up a floating menu.

At the bottom of the floating menu are three icons representing: New Style, Style Inspector and Manage Styles. Click on Manage Styles.

Click on the second tab (Recommend). Select what you would like to see and click Show. This will make the style show up when viewing recommended styles.