Correct, currently only static HTML files can be used for error pages (because what to do if there’s an error rendering a PHP page?). The errors directive could use some enhancements.
Yes, I think so, for the location block that applies to it in the nginx.conf. So, the one in location ~ ^/setup/index.php I think just means fastcgi /yoursiteroot/setup/index.php your_backend php and location ~ (index|get|static|report|404|503|health_check)\.php$ is basically fastcgi /index.php your_backend php basically.
No, but in the future we’re planning for the Caddyfile to support if blocks (against my better judgment, but oh well) that you could put directives into. However, there is a way to do this with rewrite, usually. That’s a lot of rewrites though! (Between you and me – on this public forum – I really hate it when web apps are designed like this, so that the web server has to do all the heavy lifting. It invites a LOT of problems. No reason it has to be like this. Sigh.)