Thanks for your reply!
Yes, i can connect from the ilias server to remote database via shell with
> mysql -u userName -p -h addrToYourDBServer
I checked if there is a client.ini.php in ../ilias/data/iliasClient ... but there is nothing. I does not create a file there. I then got suspicous and created a local mysql database (MariaDB v. 5.5.52) to check if it is a permission thing. But apparently its not. I can connect to my local database and it created the file you mentioned in the right folder.Everything looks fine with a local database.
But when i tried again with the remote db i get the same error: "-Database can't be reached. Please check the credentials and if database exists-"