Hey @cafoundationfund,
Events are assigned to organizers if you set the event’s organizer –?in other words, once you select an organizer, it is linked to the event that you set it as the organizer for.
As for downloading organizer emails, there’s not a way to do this automatically to get just the emails. You should, however, be able to use WordPress’ built-in Tools > Export feature, and export the Organizers post type. The meta information like name, email, etc. should be included the export file, the email is in the _OrganizerEmail meta field.
The other alternatives would be, as your thread title here suggests, running manual exports from your database directly. You can do this a number of ways, if you just google “Exporting data from MySQL” you’ll find a ton of different resources to learn all the different methods.
Cheers!
George