failed to open stream: Connection refused

This sounds more like you cannot access the mydomain.de domain.

Can you access the url directly?

http://mydomain.de/webservice.php?operation=getchallenge&username=admin

No Problem on the recieving end. Was my first thought too.

Works with Firefox on my Admin Terminal, returns json-Array. Tried per Lynx and Curl from server console returns json-Array.

Trying from my Laravel, error.

Also tried to pre encode with several php functions. Tried to deencode with several functions. Updated Laravel, updated php.

All to no avail. Somewhere something replaces the & with the &-amp;

BTW: The API-Server on the recieving end refuses http://mydomain.de/webservice.php?operation=getchallenge&-amp;username=admin because of the &-amp;

I did a search for "php file_get_contents ampersand" and I was surprised to find that file_get_contents actually does that by default.

There are a few results with some code to try, https://www.google.com/?gws_rd=ssl#q=php+file_get_contents+ampersand