I solved the problem today - it's very simple: When starting a second X-Server (regardless if tv-out or not), the second X-Screen is not displayed correctly, as stated in my above mail.
All you have to do now is switch back to the first X-Server (with Ctrl+Alt+F7) and then again to the newly started Server (Ctrl+Alt+F8). Sometimes you have to do this procedure two times, but it solves the problem.
This is for sure some driver bug, well - hopefully it will be fixed in the next release.
Maybe, however, that this applies only to systems (like mine) where the console is displayed on a framebuffer (linuxfb).
The tv-out works perfect, the videos are very smooth and also have the right size on my TV.
If you are interested of how to do this, have a look at:http://www.iofcea.de/cgi-bin/seite.pl?file=linuxtvout