You don't have to obey the GDPR for users outside the EU, so as long as the central storage is located in the EU (and only replicated across EU countries, which is easily configurable), the author is most likely absolutely fine.
By the edge locations, I'd assume he's serving cached static files, such as his blog or tracking scripts from there using CloudFlare. Assuming CloudFlare is not falsely advertising their GDPR compliance, the author is also fine.
By the edge locations, I'd assume he's serving cached static files, such as his blog or tracking scripts from there using CloudFlare. Assuming CloudFlare is not falsely advertising their GDPR compliance, the author is also fine.