Can we customize the tab headings of the tabs in the App Store? If so, is this done via site CSS or in the theme?
Sure, you can customize them via site CSS or the theme. We recommend to put your customization into a theme, because then the code is under version control, you can reproduce the customization on several stages (dev, test, prod) by using the same theme and you’re able to switch themes/stylings easily for the hole instance or a particular space.