Can wrong file permissions cause a 500 error?

Yes. Wrong ownership or mode on var/, generated/, pub/static or app/etc blocks Magento from writing cache, logs or compiled code, which surfaces as a 500. This is one of the most common post-deploy and post-restore causes. We reset permissions to the Magento-recommended scheme (writable dirs 770/660, code 750/640, correct web-server group) rather than the dangerous chmod -R 777 shortcut, and confirm the web server can write again.