But i can't connect to it by entering the IP address of the server.
That is a problem and most likely a firewall NAT one.
It's strange to me that I have to open just one port.
And how does the server do the file transfers through UDP?
I have another idea why it should'n work. The router does not accept the ping requests, is it a serious problem, or I have to search the error in somewhere else?
The Quake engine does only require one incomming port and uses it both for information exchange, playing, pinging and file transfer.
While the server can transfer files over UDP, it is much faster to set HTTP/FTP redirect up. The web server hosting the HTTP or FTP server will of course need an extra port.
You don't have to worry about standard ping packets... they are not used. Only the one port. Try scanning from the outside to see if the port responds.