@octopus, many thanks for your guidance. I did a complete new setup yesterday evening and now I got it working. The only problem I do face is an "error routing conflict"; but I guess I can live with it as the VPN is working fine.
I also get sometimes a routing conflict and I figured that this occurs after switching the "service state" to off and on.
Turning the openvpn client, a host route will remain ( the very first in "route -n" output ).
I deleted this route by "route delete <IP of VPN-provider> gw <IP of ISP>"
Then I got no "routing conflict" anymore after switching on the client.