After Alice and T-Com seemingly wanted to play ping-pong with me -- repeatedly sending me to each other -- I took the matter into my own hands and solved the problem. All DSL and Telephony problems are sorted out now. Don't ask how :D
The cable-TV issue has also vanished. I'm now using a satellite dish and the best free (as in free speech) sat receiver money can buy -- a Dreambox 7025 -- thanks to the nice folks @ Dream Multimedia TV, especially one of their core developers Felix 'tmbinc' Domke. Did I already tell you it runs a Linux Distribution built by OpenEmbedded? I'll report about my first sat experiences soon -- stay tuned.