There are many posts about nginx, re-directs, PHP, and WordPress. There are somewhat fewer posts that talk about (internal) re-writes, where the request by the web browser is mangled to be served by another resource than the one requested.
For example, I may want a request for https://mysite.foo/cool/penguin to actually be served by https://mysite.foo/coolstuff.php?id=penguin, or simply setup an alias such as https://mysite.foo/cool/penguin to be served by https://mysite.foo/cool/linux, but preserve the URL in the browser address bar.
With PHP-FPM and nginx, you run into an additional problem, which is the fastcgi_parm variables that are passed from nginx to PHP-FPM. So even if you have really fancy URL re-writing configured (and working), the end result may not be passed on to PHP-FPM from nginx.
So solve this, you should look into this construct, which is present in many nginx configurations as a default setup:
fastcgi_param REQUEST_URI $request_uri;
Since your needs probably differ from mine, I wont make this post any longer than it has to be, but that fastcgi_param line above may be a good starting point if you’re experiencing problems with nginx, PHP-FPM, and URL re-writing.
Good luck!