There is no change required in web server configuration directives (Apache, NGINX, etc.) other than ensuring minimum requirements are met.

nginx error 502 means Bad Gateway... this means the the PHP had an issue - not the nginx.

Can't browse the frontend with enabled sef as well.

Check you have this line correct

try_files $uri $uri/ /index.php?$args;

and make sure you have restarted nginx after those changes.

My bare working nginx config for development use is:

server
{
  listen 80;
  server_name remote384; #ensure your domain here is correct

  location /
  {
    root /Users/phil/Sites/remote384/;  #ensure your path here is correct
    index index.php;
    try_files $uri $uri/ /index.php?$args;
  }

   location ~ \.php
  {
    root /Users/phil/Sites/remote384/;  #ensure your path here is correct
    fastcgi_pass 127.0.0.1:9071;   #CHECK YOUR PHP PORT NUMBER 9000 by default. I have PHP 7.1 on 9071 and PHP 7.2 on 9072 etc... 
    fastcgi_index index.php;
    fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
    include fastcgi_params;
    fastcgi_split_path_info ^(.+\.php)(/.*)$;
    fastcgi_param DOCUMENT_ROOT $realpath_root;
    fastcgi_param   APPLICATION_ENV  local;  #just for my use
  }
}

(lastly I only just noticed that this was about J4... my comments are J3 comments :) )

And again, there should be no difference in NGINX/Apache/IIS configs for J3 versus J4 (the default htaccess.txt in the 4.0 branch is a bit more defensive and adds checks for modules being enabled, but that's it).

I have a lot of J3 installation on that machine and they are working fine.

I'm sorry - should have done this before:

I've turned the error reporting to development (joomla config) and i get the following error messages:
https://www.awesomescreenshot.com/image/3225449/ca53a9374818df58636a18413de9b65d

Should I disable "scream" in the php.ini in order to test?

Everyday is a school day - developing daily in PHP for over a decade now and never heard of the scream configuration param.

Yes. Disable that. It has no place in production, and arguably neither in developing a website - main use I could see of it would be in debugging only.

So did that resolve your issue?

Set to "closed" on behalf of @Quy by The JTracker Application at issues.joomla.org/joomla-cms/19876

Closing for now until further details.