1. sure you wont find anything on this in the doc. You will need to dive into the source cod of both plugins to understand how they work. In Polylang, the sync process is managed in the file admin/admin-sync.php. but it manages sync only for core entities. Understanding it can help you doing the same kind of process for GeoDirectory if you unserstand how this plugin stores its data.
2. No. The option name is the option name *in* the wp_options table.