If you set a background image, the image class can be used to change how it is stretched. See this article for options
Custom class is exactly what it says, it allows you to define a class that is applied to the category. In Lavender, this is used to position blocks in certain arragements (e.g. 3 to a row, 4 to a row, etc). In Persona, they are not used, but you can still used them if you wish to apply special styling to certain category rows.