Can a section on my app home screen show only a few chosen categories?

Yes, use the include or exclude pickers on a Categories section.

1. Go to Settings → App Settings → Mobile Home Screen.
2. Click Edit on your category section, or Add section and set Select Layout to Categories.
3. In Include Categories, search for and pick the categories to show.
4. Or use Exclude Categories to show everything except the ones you pick.
5. Click Update section (or Add section).

You can use either Include or Exclude, not both. Once one has values, the other box hides. Product, Brands and Tags sections have the same pickers.