the website the browser shows 502 - bad gateway

Did you checked this?

Yes i checked partially..

When I put a fake "index.html" in the elgg folder, then the browser works i can see that file

When i delete index.html and let it default to index.php, then i get the bad gateway, so nginx is working, so its something to do with index.php

Maybe there is some diagnostic i can run?

I checked this path its fine the folder exists (its where i put index.html from above, then removed it)

root /var/www/html/elgg;

How do i check this one below? What do i check for? How do i check SCRIPT_FILENAME and $document_root and $fastcri_script_name???

​fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;

nginx server log below (port 9000 mentioned below do i need to open it in the server firewall)

2020/05/12 17:27:34 [error] 1076#1076: *24 connect() failed (111: Connection refused) while connecting to upstream, client: 127.0.0.1, server: example.com request: "GET /index.php HTTP/1.1", upstream: "fastcgi://127.0.0.1:9000", host: "localhost"

Try this.