Thanks for writing in! All the theme options related settings and configurations are saved in the database, so there's no connection with child theme.
You need a child theme to add your own customizations to X/Pro theme's template files, so your changes will be remain separately when you're updating parent X theme. To learn more about child themes, please refer (https://theme.co/apex/forum/t/setup-how-to-setup-child-themes/57).
Hope that's clear.