Sounds like you might have something conflicting here. There’s no way a 0kb file could be downloaded as, even if there’s no content to export, it will still generate a file with the export headers in it.
Does your default export tool work? Have you tried with a default theme and all other plugins deactivated?
If possible, could you please test this like I mentioned above? If not, I’m going to assume it’s a localised problem on your site as I cannot replicate it anywhere.
I’m going to mark this query as resolved because you have not replied in a week. Feel free to respond if you are still having an issue.
