To sync it to a table you own, they'll need to set up a view where they've turned on "Allow data in this view to be synced to other bases.", and you'll then use that link to sync it. You can send them this link to Airtable's documentation if they ask how: https://support.airtable.com/docs/getting-started-with-airtable-sync
Triggering the Zap requires you to be a collaborator in some form and it doesn't sound like you're a collaborator on this base right now I'm afraid. Once you do the sync thing above you'll be able to trigger the Zap off your own table
