we are working in a sandbox on a subdomain address to later move to the main domain. The theme is asking for online theme registration. can we register on the subdomain and then change to the main address?
You could but make sure you use “staging” sub-domain name or to make sure use folder instead /staging
If you have any issue after, contact the item author for the support.
We are working with the theme in a sandbox and then taking it to production on a website that is already running Wordpress, is there an option in the theme to export the settings that were made in the sandbox?
Depending on the theme but yes. Most of the theme has feature to import/export the theme settings. For the details, refer the documentation.